Kalkulus Contoh

$\int_{0}^{π} 5 \sin^{2} (t) \cos^{4} (t) d t$

Langkah 1

Karena $5$ konstan terhadap $t$ , pindahkan $5$ keluar dari integral.

$5 \int_{0}^{π} \sin^{2} (t) \cos^{4} (t) d t$

Langkah 2

Sederhanakan dengan memfaktorkan.

Ketuk untuk lebih banyak langkah...

Langkah 2.1

Faktorkan $2$ dari $4$ .

$5 \int_{0}^{π} \sin^{2} (t) {\cos (t)}^{2 (2)} d t$

Langkah 2.2

Tulis kembali ${\cos (t)}^{2 (2)}$ sebagai eksponensiasi.

$5 \int_{0}^{π} \sin^{2} (t) {(\cos^{2} (t))}^{2} d t$

Langkah 3

Gunakan rumus setengah sudut untuk menuliskan kembali $\cos^{2} (t)$ sebagai $\frac{1 + \cos (2 t)}{2}$ .

$5 \int_{0}^{π} \sin^{2} (t) {(\frac{1 + \cos (2 t)}{2})}^{2} d t$

Langkah 4

Gunakan rumus setengah sudut untuk menuliskan kembali $\sin^{2} (t)$ sebagai $\frac{1 - \cos (2 t)}{2}$ .

$5 \int_{0}^{π} \frac{1 - \cos (2 t)}{2} {(\frac{1 + \cos (2 t)}{2})}^{2} d t$

Langkah 5

Biarkan $u_{1} = 2 t$ . Kemudian $d u_{1} = 2 d t$ sehingga $\frac{1}{2} d u_{1} = d t$ . Tulis kembali menggunakan $u_{1}$ dan $d$ $u_{1}$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.1

Biarkan $u_{1} = 2 t$ . Tentukan $\frac{d u_{1}}{d t}$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.1.1

Diferensialkan $2 t$ .

$\frac{d}{d t} [2 t]$

Langkah 5.1.2

Karena $2$ konstan terhadap $t$ , turunan dari $2 t$ terhadap $t$ adalah $2 \frac{d}{d t} [t]$ .

$2 \frac{d}{d t} [t]$

Langkah 5.1.3

Diferensialkan menggunakan Kaidah Pangkat yang menyatakan bahwa $\frac{d}{d t} [t^{n}]$ adalah $n t^{n - 1}$ di mana $n = 1$ .

$2 \cdot 1$

Langkah 5.1.4

Kalikan $2$ dengan $1$ .

$2$

Langkah 5.2

Substitusikan batas bawah untuk $t$ di $u_{1} = 2 t$ .

$u_{lower} = 2 \cdot 0$

Langkah 5.3

Kalikan $2$ dengan $0$ .

$u_{lower} = 0$

Langkah 5.4

Substitusikan batas atas untuk $t$ di $u_{1} = 2 t$ .

$u_{upper} = 2 π$

Langkah 5.5

Nilai-nilai yang ditemukan untuk $u_{lower}$ dan $u_{upper}$ akan digunakan untuk mengevaluasi integral tentunya.

$u_{lower} = 0$

$u_{upper} = 2 π$

Langkah 5.6

Tulis kembali soalnya menggunakan $u_{1}$ , $d u_{1}$ , dan batas integral yang baru.

$5 \int_{0}^{2 π} \frac{1 - \cos (u_{1})}{2} {(\frac{1 + \cos (u_{1})}{2})}^{2} \frac{1}{2} d u_{1}$

Langkah 6

Sederhanakan dengan mengalikan semuanya.

Ketuk untuk lebih banyak langkah...

Langkah 6.1

Sederhanakan.

Ketuk untuk lebih banyak langkah...

Langkah 6.1.1

Kalikan $\frac{1}{2}$ dengan $\frac{1 - \cos (u_{1})}{2}$ .

$5 \int_{0}^{2 π} \frac{1 - \cos (u_{1})}{2 \cdot 2} {(\frac{1 + \cos (u_{1})}{2})}^{2} d u_{1}$

Langkah 6.1.2

Kalikan $2$ dengan $2$ .

$5 \int_{0}^{2 π} \frac{1 - \cos (u_{1})}{4} {(\frac{1 + \cos (u_{1})}{2})}^{2} d u_{1}$

Langkah 6.2

Sederhanakan dengan saling menukar.

Ketuk untuk lebih banyak langkah...

Langkah 6.2.1

Tulis kembali $\frac{1 - \cos (u_{1})}{4}$ sebagai hasil kali.

$5 \int_{0}^{2 π} \frac{1}{4} \cdot (1 - \cos (u_{1})) {(\frac{1 + \cos (u_{1})}{2})}^{2} d u_{1}$

Langkah 6.2.2

Tulis kembali $\frac{1 + \cos (u_{1})}{2}$ sebagai hasil kali.

$5 \int_{0}^{2 π} \frac{1}{4} \cdot (1 - \cos (u_{1})) {(\frac{1}{2} \cdot (1 + \cos (u_{1})))}^{2} d u_{1}$

Langkah 6.3

Perluas $\frac{1}{4} \cdot (1 - \cos (u_{1})) {(\frac{1}{2} \cdot (1 + \cos (u_{1})))}^{2}$ .

Ketuk untuk lebih banyak langkah...

Langkah 6.3.1

Tulis kembali eksponensiasinya sebagai hasil kali.

$5 \int_{0}^{2 π} \frac{1}{4} \cdot (1 - \cos (u_{1})) (\frac{1}{2} \cdot (1 + \cos (u_{1})) (\frac{1}{2} \cdot (1 + \cos (u_{1})))) d u_{1}$

Langkah 6.3.2

Terapkan sifat distributif.

$5 \int_{0}^{2 π} (\frac{1}{4} \cdot 1 + \frac{1}{4} \cdot (- \cos (u_{1}))) (\frac{1}{2} \cdot (1 + \cos (u_{1})) (\frac{1}{2} \cdot (1 + \cos (u_{1})))) d u_{1}$

Langkah 6.3.3

Terapkan sifat distributif.

$5 \int_{0}^{2 π} (\frac{1}{4} \cdot 1 + \frac{1}{4} \cdot (- \cos (u_{1}))) ((\frac{1}{2} \cdot 1 + \frac{1}{2} \cdot \cos (u_{1})) (\frac{1}{2} \cdot (1 + \cos (u_{1})))) d u_{1}$

Langkah 6.3.4

Terapkan sifat distributif.

$5 \int_{0}^{2 π} (\frac{1}{4} \cdot 1 + \frac{1}{4} \cdot (- \cos (u_{1}))) ((\frac{1}{2} \cdot 1 + \frac{1}{2} \cdot \cos (u_{1})) (\frac{1}{2} \cdot 1 + \frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.5

Terapkan sifat distributif.

$5 \int_{0}^{2 π} (\frac{1}{4} \cdot 1 + \frac{1}{4} \cdot (- \cos (u_{1}))) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1 + \frac{1}{2} \cdot \cos (u_{1})) + \frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1 + \frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.6

Terapkan sifat distributif.

$5 \int_{0}^{2 π} (\frac{1}{4} \cdot 1 + \frac{1}{4} \cdot (- \cos (u_{1}))) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1})) + \frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1 + \frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.7

Terapkan sifat distributif.

Langkah 6.3.8

Terapkan sifat distributif.

$5 \int_{0}^{2 π} \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1})) + \frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1})) + \frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.9

Terapkan sifat distributif.

$5 \int_{0}^{2 π} \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1})) + \frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.10

Terapkan sifat distributif.

$5 \int_{0}^{2 π} \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1})) + \frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.11

Terapkan sifat distributif.

$5 \int_{0}^{2 π} \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1})) + \frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.12

Terapkan sifat distributif.

$5 \int_{0}^{2 π} \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.13

Terapkan sifat distributif.

$5 \int_{0}^{2 π} \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.14

Terapkan sifat distributif.

$5 \int_{0}^{2 π} \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.15

Susun kembali $\frac{1}{4}$ dan $1$ .

$5 \int_{0}^{2 π} 1 \cdot \frac{1}{4} (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.16

Susun kembali $\frac{1}{2}$ dan $1$ .

$5 \int_{0}^{2 π} 1 \cdot \frac{1}{4} (1 \cdot \frac{1}{2} (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.17

Susun kembali $\frac{1}{2}$ dan $1$ .

$5 \int_{0}^{2 π} 1 \cdot \frac{1}{4} (1 \cdot \frac{1}{2} (1 \cdot \frac{1}{2})) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.18

Pindahkan $\frac{1}{2}$ .

$5 \int_{0}^{2 π} 1 \cdot \frac{1}{4} (1 \cdot 1 \frac{1}{2} \cdot \frac{1}{2}) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.19

Pindahkan tanda kurung.

$5 \int_{0}^{2 π} 1 \cdot \frac{1}{4} (1 \cdot 1 \frac{1}{2}) \cdot \frac{1}{2} + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.20

Pindahkan tanda kurung.

$5 \int_{0}^{2 π} 1 \cdot \frac{1}{4} (1 \cdot 1) \frac{1}{2} \cdot \frac{1}{2} + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.21

Pindahkan $\frac{1}{4}$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.22

Susun kembali $\frac{1}{4}$ dan $1$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.23

Susun kembali $\frac{1}{2}$ dan $1$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} (1 \cdot \frac{1}{2} (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.24

Pindahkan tanda kurung.

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} (1 \cdot \frac{1}{2} \frac{1}{2}) \cdot \cos (u_{1}) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.25

Pindahkan tanda kurung.

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} (1 \cdot \frac{1}{2}) \frac{1}{2} \cdot \cos (u_{1}) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.26

Pindahkan $\frac{1}{4}$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.27

Susun kembali $\frac{1}{4}$ dan $1$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot \frac{1}{4} (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.28

Susun kembali $\frac{1}{2}$ dan $1$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot \frac{1}{4} (\frac{1}{2} \cdot \cos (u_{1}) (1 \cdot \frac{1}{2})) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.29

Pindahkan $\cos (u_{1})$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot \frac{1}{4} (\frac{1}{2} \cdot 1 \cos (u_{1}) \cdot \frac{1}{2}) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.30

Susun kembali $\frac{1}{2}$ dan $1$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot \frac{1}{4} (1 \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2}) + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.31

Pindahkan tanda kurung.

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot \frac{1}{4} (1 \cdot \frac{1}{2} \cos (u_{1})) \cdot \frac{1}{2} + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.32

Pindahkan tanda kurung.

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot \frac{1}{4} (1 \cdot \frac{1}{2}) \cos (u_{1}) \cdot \frac{1}{2} + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.33

Pindahkan $\frac{1}{4}$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + \frac{1}{4} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.34

Susun kembali $\frac{1}{4}$ dan $1$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.35

Pindahkan tanda kurung.

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} (\frac{1}{2} \cdot \cos (u_{1}) \frac{1}{2}) \cdot \cos (u_{1}) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.36

Pindahkan tanda kurung.

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} (\frac{1}{2} \cdot \cos (u_{1})) \frac{1}{2} \cdot \cos (u_{1}) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.37

Susun kembali $\frac{1}{4}$ dan $- 1$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} \frac{1}{2} \cdot \cos (u_{1}) \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot \frac{1}{4} \cos (u_{1}) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.38

Susun kembali $\frac{1}{2}$ dan $1$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} \frac{1}{2} \cdot \cos (u_{1}) \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot \frac{1}{4} \cos (u_{1}) (1 \cdot \frac{1}{2} (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.39

Susun kembali $\frac{1}{2}$ dan $1$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} \frac{1}{2} \cdot \cos (u_{1}) \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot \frac{1}{4} \cos (u_{1}) (1 \cdot \frac{1}{2} (1 \cdot \frac{1}{2})) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.40

Pindahkan $\frac{1}{2}$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} \frac{1}{2} \cdot \cos (u_{1}) \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot \frac{1}{4} \cos (u_{1}) (1 \cdot 1 \frac{1}{2} \cdot \frac{1}{2}) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.41

Pindahkan tanda kurung.

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} \frac{1}{2} \cdot \cos (u_{1}) \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot \frac{1}{4} \cos (u_{1}) (1 \cdot 1 \frac{1}{2}) \cdot \frac{1}{2} + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.42

Pindahkan tanda kurung.

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} \frac{1}{2} \cdot \cos (u_{1}) \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot \frac{1}{4} \cos (u_{1}) (1 \cdot 1) \frac{1}{2} \cdot \frac{1}{2} + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.43

Pindahkan $\cos (u_{1})$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} \frac{1}{2} \cdot \cos (u_{1}) \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot \frac{1}{4} \cdot 1 \cdot 1 \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.44

Pindahkan $\frac{1}{4}$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} \frac{1}{2} \cdot \cos (u_{1}) \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.45

Susun kembali $\frac{1}{4}$ dan $- 1$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} \frac{1}{2} \cdot \cos (u_{1}) \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot \frac{1}{4} \cos (u_{1}) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.46

Susun kembali $\frac{1}{2}$ dan $1$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} \frac{1}{2} \cdot \cos (u_{1}) \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot \frac{1}{4} \cos (u_{1}) (1 \cdot \frac{1}{2} (\frac{1}{2} \cdot \cos (u_{1}))) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.47

Pindahkan tanda kurung.

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} \frac{1}{2} \cdot \cos (u_{1}) \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot \frac{1}{4} \cos (u_{1}) (1 \cdot \frac{1}{2} \frac{1}{2}) \cdot \cos (u_{1}) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.48

Pindahkan tanda kurung.

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} \frac{1}{2} \cdot \cos (u_{1}) \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot \frac{1}{4} \cos (u_{1}) (1 \cdot \frac{1}{2}) \frac{1}{2} \cdot \cos (u_{1}) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.49

Pindahkan $\cos (u_{1})$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} \frac{1}{2} \cdot \cos (u_{1}) \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot \frac{1}{4} \cdot 1 \cos (u_{1}) \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.50

Pindahkan $\frac{1}{4}$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} \frac{1}{2} \cdot \cos (u_{1}) \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.51

Susun kembali $\frac{1}{4}$ dan $- 1$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} \frac{1}{2} \cdot \cos (u_{1}) \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot \frac{1}{4} \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.52

Susun kembali $\frac{1}{2}$ dan $1$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} \frac{1}{2} \cdot \cos (u_{1}) \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot \frac{1}{4} \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}) (1 \cdot \frac{1}{2})) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.53

Pindahkan $\cos (u_{1})$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} \frac{1}{2} \cdot \cos (u_{1}) \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot \frac{1}{4} \cos (u_{1}) (\frac{1}{2} \cdot 1 \cos (u_{1}) \cdot \frac{1}{2}) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.54

Susun kembali $\frac{1}{2}$ dan $1$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} \frac{1}{2} \cdot \cos (u_{1}) \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot \frac{1}{4} \cos (u_{1}) (1 \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2}) + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.55

Pindahkan tanda kurung.

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} \frac{1}{2} \cdot \cos (u_{1}) \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot \frac{1}{4} \cos (u_{1}) (1 \cdot \frac{1}{2} \cos (u_{1})) \cdot \frac{1}{2} + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.56

Pindahkan tanda kurung.

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} \frac{1}{2} \cdot \cos (u_{1}) \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot \frac{1}{4} \cos (u_{1}) (1 \cdot \frac{1}{2}) \cos (u_{1}) \cdot \frac{1}{2} + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.57

Pindahkan $\cos (u_{1})$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} \frac{1}{2} \cdot \cos (u_{1}) \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot \frac{1}{4} \cdot 1 \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.58

Pindahkan $\frac{1}{4}$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} \frac{1}{2} \cdot \cos (u_{1}) \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + \frac{1}{4} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.59

Susun kembali $\frac{1}{4}$ dan $- 1$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} \frac{1}{2} \cdot \cos (u_{1}) \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} - 1 \cdot \frac{1}{4} \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}))) d u_{1}$

Langkah 6.3.60

Pindahkan tanda kurung.

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} \frac{1}{2} \cdot \cos (u_{1}) \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} - 1 \cdot \frac{1}{4} \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1}) \frac{1}{2}) \cdot \cos (u_{1}) d u_{1}$

Langkah 6.3.61

Pindahkan tanda kurung.

$5 \int_{0}^{2 π} 1 \cdot 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} \frac{1}{2} \cdot \cos (u_{1}) \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \cdot \frac{1}{2} \frac{1}{2} \cdot \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} - 1 \cdot \frac{1}{4} \cos (u_{1}) (\frac{1}{2} \cdot \cos (u_{1})) \frac{1}{2} \cdot \cos (u_{1}) d u_{1}$

Langkah 6.3.62

Kalikan $1$ dengan $1$ .

$5 \int_{0}^{2 π} 1 \cdot 1 \frac{1}{4} \frac{1}{2} \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \frac{1}{2} \frac{1}{2} \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 (\frac{1}{4}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.63

Kalikan $1$ dengan $1$ .

$5 \int_{0}^{2 π} 1 (\frac{1}{4}) \frac{1}{2} \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \frac{1}{2} \frac{1}{2} \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 (\frac{1}{4}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.64

Kalikan $\frac{1}{4}$ dengan $1$ .

$5 \int_{0}^{2 π} \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \frac{1}{2} \frac{1}{2} \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 (\frac{1}{4}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.65

Kalikan $\frac{1}{4}$ dengan $\frac{1}{2}$ .

$5 \int_{0}^{2 π} \frac{1}{4 \cdot 2} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \frac{1}{2} \frac{1}{2} \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 (\frac{1}{4}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.66

Kalikan $4$ dengan $2$ .

$5 \int_{0}^{2 π} \frac{1}{8} \cdot \frac{1}{2} + 1 \cdot 1 \frac{1}{4} \frac{1}{2} \frac{1}{2} \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 (\frac{1}{4}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.67

Kalikan $\frac{1}{8}$ dengan $\frac{1}{2}$ .

$5 \int_{0}^{2 π} \frac{1}{8 \cdot 2} + 1 \cdot 1 \frac{1}{4} \frac{1}{2} \frac{1}{2} \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 (\frac{1}{4}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.68

Kalikan $8$ dengan $2$ .

$5 \int_{0}^{2 π} \frac{1}{16} + 1 \cdot 1 \frac{1}{4} \frac{1}{2} \frac{1}{2} \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 (\frac{1}{4}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.69

Kalikan $1$ dengan $1$ .

$5 \int_{0}^{2 π} \frac{1}{16} + 1 (\frac{1}{4}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 (\frac{1}{4}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.70

Kalikan $\frac{1}{4}$ dengan $1$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{1}{4} \cdot \frac{1}{2} \frac{1}{2} \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 (\frac{1}{4}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.71

Kalikan $\frac{1}{4}$ dengan $\frac{1}{2}$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{1}{4 \cdot 2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 (\frac{1}{4}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.72

Kalikan $4$ dengan $2$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{1}{8} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 (\frac{1}{4}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.73

Kalikan $\frac{1}{8}$ dengan $\frac{1}{2}$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{1}{8 \cdot 2} \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 (\frac{1}{4}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.74

Kalikan $8$ dengan $2$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{1}{16} \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 (\frac{1}{4}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.75

Gabungkan $\frac{1}{16}$ dan $\cos (u_{1})$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{\cos (u_{1})}{16} + 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 (\frac{1}{4}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.76

Kalikan $1$ dengan $1$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{\cos (u_{1})}{16} + 1 (\frac{1}{4}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 (\frac{1}{4}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.77

Kalikan $\frac{1}{4}$ dengan $1$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{\cos (u_{1})}{16} + \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 (\frac{1}{4}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.78

Kalikan $\frac{1}{4}$ dengan $\frac{1}{2}$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{\cos (u_{1})}{16} + \frac{1}{4 \cdot 2} \cos (u_{1}) \frac{1}{2} + 1 (\frac{1}{4}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.79

Kalikan $4$ dengan $2$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{\cos (u_{1})}{16} + \frac{1}{8} \cos (u_{1}) \frac{1}{2} + 1 (\frac{1}{4}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.80

Gabungkan $\frac{1}{8}$ dan $\cos (u_{1})$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos (u_{1})}{8} \cdot \frac{1}{2} + 1 (\frac{1}{4}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.81

Kalikan $\frac{\cos (u_{1})}{8}$ dengan $\frac{1}{2}$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos (u_{1})}{8 \cdot 2} + 1 (\frac{1}{4}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.82

Kalikan $8$ dengan $2$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos (u_{1})}{16} + 1 (\frac{1}{4}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.83

Kalikan $\frac{1}{4}$ dengan $1$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos (u_{1})}{16} + \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.84

Kalikan $\frac{1}{4}$ dengan $\frac{1}{2}$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos (u_{1})}{16} + \frac{1}{4 \cdot 2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.85

Kalikan $4$ dengan $2$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos (u_{1})}{16} + \frac{1}{8} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.86

Gabungkan $\frac{1}{8}$ dan $\cos (u_{1})$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos (u_{1})}{8} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.87

Kalikan $\frac{\cos (u_{1})}{8}$ dengan $\frac{1}{2}$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos (u_{1})}{8 \cdot 2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.88

Kalikan $8$ dengan $2$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos (u_{1})}{16} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.89

Gabungkan $\frac{\cos (u_{1})}{16}$ dan $\cos (u_{1})$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos (u_{1}) \cos (u_{1})}{16} - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.90

Naikkan $\cos (u_{1})$ menjadi pangkat $1$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos^{1} (u_{1}) \cos (u_{1})}{16} - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.91

Naikkan $\cos (u_{1})$ menjadi pangkat $1$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos^{1} (u_{1}) \cos^{1} (u_{1})}{16} - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.92

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos (u_{1})}{16} + \frac{{\cos (u_{1})}^{1 + 1}}{16} - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.93

Tambahkan $1$ dan $1$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.94

Tambahkan $\frac{\cos (u_{1})}{16}$ dan $\frac{\cos (u_{1})}{16}$ .

$5 \int_{0}^{2 π} \frac{1}{16} + 2 \frac{\cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.95

Gabungkan $2$ dan $\frac{\cos (u_{1})}{16}$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.96

Kalikan $- 1$ dengan $1$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.97

Kalikan $- 1$ dengan $1$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.98

Gabungkan $\frac{1}{4}$ dan $\cos (u_{1})$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{4} \cdot \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.99

Gabungkan $- \frac{\cos (u_{1})}{4}$ dan $\frac{1}{2}$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{4 \cdot 2} \cdot \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.100

Kalikan $4$ dengan $2$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{8} \cdot \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.101

Gabungkan $- \frac{\cos (u_{1})}{8}$ dan $\frac{1}{2}$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{8 \cdot 2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.102

Kalikan $8$ dengan $2$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.103

Kalikan $- 1$ dengan $1$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.104

Gabungkan $\frac{1}{4}$ dan $\cos (u_{1})$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{4} \cdot \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.105

Gabungkan $- \frac{\cos (u_{1})}{4}$ dan $\frac{1}{2}$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{4 \cdot 2} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.106

Kalikan $4$ dengan $2$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{8} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.107

Gabungkan $- \frac{\cos (u_{1})}{8}$ dan $\frac{1}{2}$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{8 \cdot 2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.108

Kalikan $8$ dengan $2$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.109

Gabungkan $\frac{\cos (u_{1})}{16}$ dan $\cos (u_{1})$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1}) \cos (u_{1})}{16} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.110

Naikkan $\cos (u_{1})$ menjadi pangkat $1$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{1} (u_{1}) \cos (u_{1})}{16} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.111

Naikkan $\cos (u_{1})$ menjadi pangkat $1$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{1} (u_{1}) \cos^{1} (u_{1})}{16} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.112

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{{\cos (u_{1})}^{1 + 1}}{16} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.113

Tambahkan $1$ dan $1$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.114

Kalikan $- 1$ dengan $1$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.115

Gabungkan $\frac{1}{4}$ dan $\cos (u_{1})$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{4} \cdot \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.116

Gabungkan $- \frac{\cos (u_{1})}{4}$ dan $\frac{1}{2}$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{4 \cdot 2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.117

Kalikan $4$ dengan $2$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{8} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.118

Gabungkan $\frac{\cos (u_{1})}{8}$ dan $\cos (u_{1})$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1}) \cos (u_{1})}{8} \cdot \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.119

Naikkan $\cos (u_{1})$ menjadi pangkat $1$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos^{1} (u_{1}) \cos (u_{1})}{8} \cdot \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.120

Naikkan $\cos (u_{1})$ menjadi pangkat $1$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos^{1} (u_{1}) \cos^{1} (u_{1})}{8} \cdot \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.121

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{{\cos (u_{1})}^{1 + 1}}{8} \cdot \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.122

Tambahkan $1$ dan $1$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{8} \cdot \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.123

Gabungkan $- \frac{\cos^{2} (u_{1})}{8}$ dan $\frac{1}{2}$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{8 \cdot 2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.124

Kalikan $8$ dengan $2$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.125

Gabungkan $\frac{1}{4}$ dan $\cos (u_{1})$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - 1 \frac{\cos (u_{1})}{4} \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.126

Gabungkan $- 1 \frac{\cos (u_{1})}{4}$ dan $\frac{1}{2}$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{- 1 \frac{\cos (u_{1})}{4}}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.127

Gabungkan $\frac{- 1 \frac{\cos (u_{1})}{4}}{2}$ dan $\cos (u_{1})$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{- 1 \frac{\cos (u_{1})}{4} \cos (u_{1})}{2} \cdot \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.128

Gabungkan $\frac{\cos (u_{1})}{4}$ dan $\cos (u_{1})$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{- 1 \frac{\cos (u_{1}) \cos (u_{1})}{4}}{2} \cdot \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.129

Naikkan $\cos (u_{1})$ menjadi pangkat $1$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{- 1 \frac{\cos^{1} (u_{1}) \cos (u_{1})}{4}}{2} \cdot \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.130

Naikkan $\cos (u_{1})$ menjadi pangkat $1$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{- 1 \frac{\cos^{1} (u_{1}) \cos^{1} (u_{1})}{4}}{2} \cdot \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.131

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{- 1 \frac{{\cos (u_{1})}^{1 + 1}}{4}}{2} \cdot \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.132

Tambahkan $1$ dan $1$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{- 1 \frac{\cos^{2} (u_{1})}{4}}{2} \cdot \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 6.3.133

Kalikan $\frac{- 1 \frac{\cos^{2} (u_{1})}{4}}{2}$ dengan $\frac{1}{2}$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{- 1 \frac{\cos^{2} (u_{1})}{4}}{2 \cdot 2} \cos (u_{1}) d u_{1}$

Langkah 6.3.134

Kalikan $2$ dengan $2$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{- 1 \frac{\cos^{2} (u_{1})}{4}}{4} \cos (u_{1}) d u_{1}$

Langkah 6.3.135

Gabungkan $\frac{- 1 \frac{\cos^{2} (u_{1})}{4}}{4}$ dan $\cos (u_{1})$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{- 1 \frac{\cos^{2} (u_{1})}{4} \cos (u_{1})}{4} d u_{1}$

Langkah 6.3.136

Gabungkan $\frac{\cos^{2} (u_{1})}{4}$ dan $\cos (u_{1})$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{- 1 \frac{\cos^{2} (u_{1}) \cos (u_{1})}{4}}{4} d u_{1}$

Langkah 6.3.137

Naikkan $\cos (u_{1})$ menjadi pangkat $1$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{- 1 \frac{\cos^{2} (u_{1}) \cos^{1} (u_{1})}{4}}{4} d u_{1}$

Langkah 6.3.138

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{- 1 \frac{{\cos (u_{1})}^{2 + 1}}{4}}{4} d u_{1}$

Langkah 6.3.139

Tambahkan $2$ dan $1$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4} d u_{1}$

Langkah 6.3.140

Kurangi $\frac{\cos^{2} (u_{1})}{16}$ dengan $- \frac{\cos^{2} (u_{1})}{16}$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - 2 \frac{\cos^{2} (u_{1})}{16} + \frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4} d u_{1}$

Langkah 6.3.141

Gabungkan $- 2$ dan $\frac{\cos^{2} (u_{1})}{16}$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} + \frac{- 2 \cos^{2} (u_{1})}{16} + \frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4} d u_{1}$

Langkah 6.3.142

Susun kembali $\frac{2 \cos (u_{1})}{16}$ dan $\frac{\cos^{2} (u_{1})}{16}$ .

$5 \int_{0}^{2 π} \frac{1}{16} + \frac{\cos^{2} (u_{1})}{16} + \frac{2 \cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} + \frac{- 2 \cos^{2} (u_{1})}{16} + \frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4} d u_{1}$

Langkah 6.3.143

Susun kembali $\frac{1}{16}$ dan $\frac{\cos^{2} (u_{1})}{16}$ .

$5 \int_{0}^{2 π} \frac{\cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{2 \cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} + \frac{- 2 \cos^{2} (u_{1})}{16} + \frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4} d u_{1}$

Langkah 6.3.144

Susun kembali $\frac{- 2 \cos^{2} (u_{1})}{16}$ dan $\frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4}$ .

$5 \int_{0}^{2 π} \frac{\cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{2 \cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} + \frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4} + \frac{- 2 \cos^{2} (u_{1})}{16} d u_{1}$

Langkah 6.3.145

Pindahkan $- \frac{\cos (u_{1})}{16}$ .

$5 \int_{0}^{2 π} \frac{\cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4} + \frac{- 2 \cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} d u_{1}$

Langkah 6.3.146

Pindahkan $\frac{2 \cos (u_{1})}{16}$ .

$5 \int_{0}^{2 π} \frac{\cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4} + \frac{- 2 \cos^{2} (u_{1})}{16} + \frac{2 \cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} d u_{1}$

Langkah 6.3.147

Pindahkan $\frac{1}{16}$ .

$5 \int_{0}^{2 π} \frac{\cos^{2} (u_{1})}{16} + \frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4} + \frac{- 2 \cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{2 \cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} d u_{1}$

Langkah 6.3.148

Susun kembali $\frac{\cos^{2} (u_{1})}{16}$ dan $\frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4}$ .

$5 \int_{0}^{2 π} \frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4} + \frac{\cos^{2} (u_{1})}{16} + \frac{- 2 \cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{2 \cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} d u_{1}$

Langkah 6.3.149

Gabungkan pembilang dari penyebut persekutuan.

$5 \int_{0}^{2 π} \frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4} + \frac{\cos^{2} (u_{1}) - 2 \cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{2 \cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} d u_{1}$

Langkah 6.3.150

Kurangi $2 \cos^{2} (u_{1})$ dengan $\cos^{2} (u_{1})$ .

$5 \int_{0}^{2 π} \frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4} + \frac{- \cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{2 \cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} d u_{1}$

Langkah 6.3.151

Gabungkan pembilang dari penyebut persekutuan.

$5 \int_{0}^{2 π} \frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4} + \frac{- \cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{2 \cos (u_{1}) - \cos (u_{1})}{16} d u_{1}$

Langkah 6.3.152

Kurangi $\cos (u_{1})$ dengan $2 \cos (u_{1})$ .

$5 \int_{0}^{2 π} \frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4} + \frac{- \cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{\cos (u_{1})}{16} d u_{1}$

Langkah 6.4

Sederhanakan.

Ketuk untuk lebih banyak langkah...

Langkah 6.4.1

Tulis kembali $- 1 \frac{\cos^{3} (u_{1})}{4}$ sebagai $- \frac{\cos^{3} (u_{1})}{4}$ .

$5 \int_{0}^{2 π} \frac{- \frac{\cos^{3} (u_{1})}{4}}{4} + \frac{- \cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{\cos (u_{1})}{16} d u_{1}$

Langkah 6.4.2

Tulis kembali $\frac{- \frac{\cos^{3} (u_{1})}{4}}{4}$ sebagai hasil kali.

$5 \int_{0}^{2 π} - \frac{\cos^{3} (u_{1})}{4} \cdot \frac{1}{4} + \frac{- \cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{\cos (u_{1})}{16} d u_{1}$

Langkah 6.4.3

Kalikan $\frac{1}{4}$ dengan $\frac{\cos^{3} (u_{1})}{4}$ .

$5 \int_{0}^{2 π} - \frac{\cos^{3} (u_{1})}{4 \cdot 4} + \frac{- \cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{\cos (u_{1})}{16} d u_{1}$

Langkah 6.4.4

Kalikan $4$ dengan $4$ .

$5 \int_{0}^{2 π} - \frac{\cos^{3} (u_{1})}{16} + \frac{- \cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{\cos (u_{1})}{16} d u_{1}$

Langkah 6.4.5

Pindahkan tanda negatif di depan pecahan.

$5 \int_{0}^{2 π} - \frac{\cos^{3} (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{\cos (u_{1})}{16} d u_{1}$

Langkah 7

Bagi integral tunggal menjadi beberapa integral.

$5 (\int_{0}^{2 π} - \frac{\cos^{3} (u_{1})}{16} d u_{1} + \int_{0}^{2 π} - \frac{\cos^{2} (u_{1})}{16} d u_{1} + \int_{0}^{2 π} \frac{1}{16} d u_{1} + \int_{0}^{2 π} \frac{\cos (u_{1})}{16} d u_{1})$

Langkah 8

Karena $- 1$ konstan terhadap $u_{1}$ , pindahkan $- 1$ keluar dari integral.

$5 (- \int_{0}^{2 π} \frac{\cos^{3} (u_{1})}{16} d u_{1} + \int_{0}^{2 π} - \frac{\cos^{2} (u_{1})}{16} d u_{1} + \int_{0}^{2 π} \frac{1}{16} d u_{1} + \int_{0}^{2 π} \frac{\cos (u_{1})}{16} d u_{1})$

Langkah 9

Karena $\frac{1}{16}$ konstan terhadap $u_{1}$ , pindahkan $\frac{1}{16}$ keluar dari integral.

$5 (- (\frac{1}{16} \int_{0}^{2 π} \cos^{3} (u_{1}) d u_{1}) + \int_{0}^{2 π} - \frac{\cos^{2} (u_{1})}{16} d u_{1} + \int_{0}^{2 π} \frac{1}{16} d u_{1} + \int_{0}^{2 π} \frac{\cos (u_{1})}{16} d u_{1})$

Langkah 10

Faktorkan $\cos^{2} (u_{1})$ .

$5 (- \frac{1}{16} \int_{0}^{2 π} \cos^{2} (u_{1}) \cos (u_{1}) d u_{1} + \int_{0}^{2 π} - \frac{\cos^{2} (u_{1})}{16} d u_{1} + \int_{0}^{2 π} \frac{1}{16} d u_{1} + \int_{0}^{2 π} \frac{\cos (u_{1})}{16} d u_{1})$

Langkah 11

Menggunakan Identitas Pythagoras, tulis kembali $\cos^{2} (u_{1})$ sebagai $1 - \sin^{2} (u_{1})$ .

$5 (- \frac{1}{16} \int_{0}^{2 π} (1 - \sin^{2} (u_{1})) \cos (u_{1}) d u_{1} + \int_{0}^{2 π} - \frac{\cos^{2} (u_{1})}{16} d u_{1} + \int_{0}^{2 π} \frac{1}{16} d u_{1} + \int_{0}^{2 π} \frac{\cos (u_{1})}{16} d u_{1})$

Langkah 12

Biarkan $u_{2} = \sin (u_{1})$ . Kemudian $d u_{2} = \cos (u_{1}) d u_{1}$ sehingga $\frac{1}{\cos (u_{1})} d u_{2} = d u_{1}$ . Tulis kembali menggunakan $u_{2}$ dan $d$ $u_{2}$ .

Ketuk untuk lebih banyak langkah...

Langkah 12.1

Biarkan $u_{2} = \sin (u_{1})$ . Tentukan $\frac{d u_{2}}{d u_{1}}$ .

Ketuk untuk lebih banyak langkah...

Langkah 12.1.1

Diferensialkan $\sin (u_{1})$ .

$\frac{d}{d u_{1}} [\sin (u_{1})]$

Langkah 12.1.2

Turunan dari $\sin (u_{1})$ terhadap $u_{1}$ adalah $\cos (u_{1})$ .

$\cos (u_{1})$

Langkah 12.2

Substitusikan batas bawah untuk $u_{1}$ di $u_{2} = \sin (u_{1})$ .

$u_{lower} = \sin (0)$

Langkah 12.3

Nilai eksak dari $\sin (0)$ adalah $0$ .

$u_{lower} = 0$

Langkah 12.4

Substitusikan batas atas untuk $u_{1}$ di $u_{2} = \sin (u_{1})$ .

$u_{upper} = \sin (2 π)$

Langkah 12.5

Sederhanakan.

Ketuk untuk lebih banyak langkah...

Langkah 12.5.1

Kurangi rotasi penuh dari $2 π$ sampai sudutnya lebih besar dari atau sama dengan $0$ dan lebih kecil dari $2 π$ .

$u_{upper} = \sin (0)$

Langkah 12.5.2

Nilai eksak dari $\sin (0)$ adalah $0$ .

$u_{upper} = 0$

Langkah 12.6

Nilai-nilai yang ditemukan untuk $u_{lower}$ dan $u_{upper}$ akan digunakan untuk mengevaluasi integral tentunya.

$u_{lower} = 0$

$u_{upper} = 0$

Langkah 12.7

Tulis kembali soalnya menggunakan $u_{2}$ , $d u_{2}$ , dan batas integral yang baru.

$5 (- \frac{1}{16} \int_{0}^{0} 1 - {u_{2}}^{2} d u_{2} + \int_{0}^{2 π} - \frac{\cos^{2} (u_{1})}{16} d u_{1} + \int_{0}^{2 π} \frac{1}{16} d u_{1} + \int_{0}^{2 π} \frac{\cos (u_{1})}{16} d u_{1})$

Langkah 13

Bagi integral tunggal menjadi beberapa integral.

$5 (- \frac{1}{16} (\int_{0}^{0} d u_{2} + \int_{0}^{0} - {u_{2}}^{2} d u_{2}) + \int_{0}^{2 π} - \frac{\cos^{2} (u_{1})}{16} d u_{1} + \int_{0}^{2 π} \frac{1}{16} d u_{1} + \int_{0}^{2 π} \frac{\cos (u_{1})}{16} d u_{1})$

Langkah 14

Terapkan aturan konstanta.

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} + \int_{0}^{0} - {u_{2}}^{2} d u_{2}) + \int_{0}^{2 π} - \frac{\cos^{2} (u_{1})}{16} d u_{1} + \int_{0}^{2 π} \frac{1}{16} d u_{1} + \int_{0}^{2 π} \frac{\cos (u_{1})}{16} d u_{1})$

Langkah 15

Karena $- 1$ konstan terhadap $u_{2}$ , pindahkan $- 1$ keluar dari integral.

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} - \int_{0}^{0} {u_{2}}^{2} d u_{2}) + \int_{0}^{2 π} - \frac{\cos^{2} (u_{1})}{16} d u_{1} + \int_{0}^{2 π} \frac{1}{16} d u_{1} + \int_{0}^{2 π} \frac{\cos (u_{1})}{16} d u_{1})$

Langkah 16

Menurut Kaidah Pangkat, integral dari ${u_{2}}^{2}$ terhadap $u_{2}$ adalah $\frac{1}{3} {u_{2}}^{3}$ .

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} - (\frac{1}{3} {u_{2}}^{3}]_{0}^{0})) + \int_{0}^{2 π} - \frac{\cos^{2} (u_{1})}{16} d u_{1} + \int_{0}^{2 π} \frac{1}{16} d u_{1} + \int_{0}^{2 π} \frac{\cos (u_{1})}{16} d u_{1})$

Langkah 17

Gabungkan $\frac{1}{3}$ dan ${u_{2}}^{3}$ .

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} - (\frac{{u_{2}}^{3}}{3}]_{0}^{0})) + \int_{0}^{2 π} - \frac{\cos^{2} (u_{1})}{16} d u_{1} + \int_{0}^{2 π} \frac{1}{16} d u_{1} + \int_{0}^{2 π} \frac{\cos (u_{1})}{16} d u_{1})$

Langkah 18

Karena $- 1$ konstan terhadap $u_{1}$ , pindahkan $- 1$ keluar dari integral.

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} - (\frac{{u_{2}}^{3}}{3}]_{0}^{0})) - \int_{0}^{2 π} \frac{\cos^{2} (u_{1})}{16} d u_{1} + \int_{0}^{2 π} \frac{1}{16} d u_{1} + \int_{0}^{2 π} \frac{\cos (u_{1})}{16} d u_{1})$

Langkah 19

Karena $\frac{1}{16}$ konstan terhadap $u_{1}$ , pindahkan $\frac{1}{16}$ keluar dari integral.

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} - (\frac{{u_{2}}^{3}}{3}]_{0}^{0})) - (\frac{1}{16} \int_{0}^{2 π} \cos^{2} (u_{1}) d u_{1}) + \int_{0}^{2 π} \frac{1}{16} d u_{1} + \int_{0}^{2 π} \frac{\cos (u_{1})}{16} d u_{1})$

Langkah 20

Gunakan rumus setengah sudut untuk menuliskan kembali $\cos^{2} (u_{1})$ sebagai $\frac{1 + \cos (2 u_{1})}{2}$ .

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} - (\frac{{u_{2}}^{3}}{3}]_{0}^{0})) - \frac{1}{16} \int_{0}^{2 π} \frac{1 + \cos (2 u_{1})}{2} d u_{1} + \int_{0}^{2 π} \frac{1}{16} d u_{1} + \int_{0}^{2 π} \frac{\cos (u_{1})}{16} d u_{1})$

Langkah 21

Karena $\frac{1}{2}$ konstan terhadap $u_{1}$ , pindahkan $\frac{1}{2}$ keluar dari integral.

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} - (\frac{{u_{2}}^{3}}{3}]_{0}^{0})) - \frac{1}{16} (\frac{1}{2} \int_{0}^{2 π} 1 + \cos (2 u_{1}) d u_{1}) + \int_{0}^{2 π} \frac{1}{16} d u_{1} + \int_{0}^{2 π} \frac{\cos (u_{1})}{16} d u_{1})$

Langkah 22

Sederhanakan.

Ketuk untuk lebih banyak langkah...

Langkah 22.1

Kalikan $\frac{1}{2}$ dengan $\frac{1}{16}$ .

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} - (\frac{{u_{2}}^{3}}{3}]_{0}^{0})) - \frac{1}{2 \cdot 16} \int_{0}^{2 π} 1 + \cos (2 u_{1}) d u_{1} + \int_{0}^{2 π} \frac{1}{16} d u_{1} + \int_{0}^{2 π} \frac{\cos (u_{1})}{16} d u_{1})$

Langkah 22.2

Kalikan $2$ dengan $16$ .

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} - (\frac{{u_{2}}^{3}}{3}]_{0}^{0})) - \frac{1}{32} \int_{0}^{2 π} 1 + \cos (2 u_{1}) d u_{1} + \int_{0}^{2 π} \frac{1}{16} d u_{1} + \int_{0}^{2 π} \frac{\cos (u_{1})}{16} d u_{1})$

Langkah 23

Bagi integral tunggal menjadi beberapa integral.

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} - (\frac{{u_{2}}^{3}}{3}]_{0}^{0})) - \frac{1}{32} (\int_{0}^{2 π} d u_{1} + \int_{0}^{2 π} \cos (2 u_{1}) d u_{1}) + \int_{0}^{2 π} \frac{1}{16} d u_{1} + \int_{0}^{2 π} \frac{\cos (u_{1})}{16} d u_{1})$

Langkah 24

Terapkan aturan konstanta.

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} - (\frac{{u_{2}}^{3}}{3}]_{0}^{0})) - \frac{1}{32} (u_{1}]_{0}^{2 π} + \int_{0}^{2 π} \cos (2 u_{1}) d u_{1}) + \int_{0}^{2 π} \frac{1}{16} d u_{1} + \int_{0}^{2 π} \frac{\cos (u_{1})}{16} d u_{1})$

Langkah 25

Biarkan $u_{3} = 2 u_{1}$ . Kemudian $d u_{3} = 2 d u_{1}$ sehingga $\frac{1}{2} d u_{3} = d u_{1}$ . Tulis kembali menggunakan $u_{3}$ dan $d$ $u_{3}$ .

Ketuk untuk lebih banyak langkah...

Langkah 25.1

Biarkan $u_{3} = 2 u_{1}$ . Tentukan $\frac{d u_{3}}{d u_{1}}$ .

Ketuk untuk lebih banyak langkah...

Langkah 25.1.1

Diferensialkan $2 u_{1}$ .

$\frac{d}{d u_{1}} [2 u_{1}]$

Langkah 25.1.2

Karena $2$ konstan terhadap $u_{1}$ , turunan dari $2 u_{1}$ terhadap $u_{1}$ adalah $2 \frac{d}{d u_{1}} [u_{1}]$ .

$2 \frac{d}{d u_{1}} [u_{1}]$

Langkah 25.1.3

Diferensialkan menggunakan Kaidah Pangkat yang menyatakan bahwa $\frac{d}{d u_{1}} [{u_{1}}^{n}]$ adalah $n {u_{1}}^{n - 1}$ di mana $n = 1$ .

$2 \cdot 1$

Langkah 25.1.4

Kalikan $2$ dengan $1$ .

$2$

Langkah 25.2

Substitusikan batas bawah untuk $u_{1}$ di $u_{3} = 2 u_{1}$ .

$u_{lower} = 2 \cdot 0$

Langkah 25.3

Kalikan $2$ dengan $0$ .

$u_{lower} = 0$

Langkah 25.4

Substitusikan batas atas untuk $u_{1}$ di $u_{3} = 2 u_{1}$ .

$u_{upper} = 2 (2 π)$

Langkah 25.5

Kalikan $2$ dengan $2$ .

$u_{upper} = 4 π$

Langkah 25.6

Nilai-nilai yang ditemukan untuk $u_{lower}$ dan $u_{upper}$ akan digunakan untuk mengevaluasi integral tentunya.

$u_{lower} = 0$

$u_{upper} = 4 π$

Langkah 25.7

Tulis kembali soalnya menggunakan $u_{3}$ , $d u_{3}$ , dan batas integral yang baru.

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} - (\frac{{u_{2}}^{3}}{3}]_{0}^{0})) - \frac{1}{32} (u_{1}]_{0}^{2 π} + \int_{0}^{4 π} \cos (u_{3}) \frac{1}{2} d u_{3}) + \int_{0}^{2 π} \frac{1}{16} d u_{1} + \int_{0}^{2 π} \frac{\cos (u_{1})}{16} d u_{1})$

Langkah 26

Gabungkan $\cos (u_{3})$ dan $\frac{1}{2}$ .

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} - (\frac{{u_{2}}^{3}}{3}]_{0}^{0})) - \frac{1}{32} (u_{1}]_{0}^{2 π} + \int_{0}^{4 π} \frac{\cos (u_{3})}{2} d u_{3}) + \int_{0}^{2 π} \frac{1}{16} d u_{1} + \int_{0}^{2 π} \frac{\cos (u_{1})}{16} d u_{1})$

Langkah 27

Karena $\frac{1}{2}$ konstan terhadap $u_{3}$ , pindahkan $\frac{1}{2}$ keluar dari integral.

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} - (\frac{{u_{2}}^{3}}{3}]_{0}^{0})) - \frac{1}{32} (u_{1}]_{0}^{2 π} + \frac{1}{2} \int_{0}^{4 π} \cos (u_{3}) d u_{3}) + \int_{0}^{2 π} \frac{1}{16} d u_{1} + \int_{0}^{2 π} \frac{\cos (u_{1})}{16} d u_{1})$

Langkah 28

Integral dari $\cos (u_{3})$ terhadap $u_{3}$ adalah $\sin (u_{3})$ .

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} - (\frac{{u_{2}}^{3}}{3}]_{0}^{0})) - \frac{1}{32} (u_{1}]_{0}^{2 π} + \frac{1}{2} \sin (u_{3})]_{0}^{4 π}) + \int_{0}^{2 π} \frac{1}{16} d u_{1} + \int_{0}^{2 π} \frac{\cos (u_{1})}{16} d u_{1})$

Langkah 29

Gabungkan $\frac{1}{2}$ dan $\sin (u_{3})]_{0}^{4 π}$ .

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} - (\frac{{u_{2}}^{3}}{3}]_{0}^{0})) - \frac{1}{32} (u_{1}]_{0}^{2 π} + \frac{\sin (u_{3})]_{0}^{4 π}}{2}) + \int_{0}^{2 π} \frac{1}{16} d u_{1} + \int_{0}^{2 π} \frac{\cos (u_{1})}{16} d u_{1})$

Langkah 30

Terapkan aturan konstanta.

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} - (\frac{{u_{2}}^{3}}{3}]_{0}^{0})) - \frac{1}{32} (u_{1}]_{0}^{2 π} + \frac{\sin (u_{3})]_{0}^{4 π}}{2}) + \frac{1}{16} u_{1}]_{0}^{2 π} + \int_{0}^{2 π} \frac{\cos (u_{1})}{16} d u_{1})$

Langkah 31

Gabungkan $\frac{1}{16}$ dan $u_{1}$ .

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} - (\frac{{u_{2}}^{3}}{3}]_{0}^{0})) - \frac{1}{32} (u_{1}]_{0}^{2 π} + \frac{\sin (u_{3})]_{0}^{4 π}}{2}) + \frac{u_{1}}{16}]_{0}^{2 π} + \int_{0}^{2 π} \frac{\cos (u_{1})}{16} d u_{1})$

Langkah 32

Karena $\frac{1}{16}$ konstan terhadap $u_{1}$ , pindahkan $\frac{1}{16}$ keluar dari integral.

Langkah 33

Integral dari $\cos (u_{1})$ terhadap $u_{1}$ adalah $\sin (u_{1})$ .

Langkah 34

Sederhanakan.

Ketuk untuk lebih banyak langkah...

Langkah 34.1

Gabungkan $\frac{1}{16}$ dan $\sin (u_{1})]_{0}^{2 π}$ .

Langkah 34.2

Untuk menuliskan $- \frac{1}{32} (u_{1}]_{0}^{2 π} + \frac{\sin (u_{3})]_{0}^{4 π}}{2})$ sebagai pecahan dengan penyebut umum, kalikan dengan $\frac{16}{16}$ .

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} - (\frac{{u_{2}}^{3}}{3}]_{0}^{0})) - \frac{1}{32} (u_{1}]_{0}^{2 π} + \frac{\sin (u_{3})]_{0}^{4 π}}{2}) \cdot \frac{16}{16} + \frac{\sin (u_{1})]_{0}^{2 π}}{16} + \frac{u_{1}}{16}]_{0}^{2 π})$

Langkah 34.3

Gabungkan $- \frac{1}{32} (u_{1}]_{0}^{2 π} + \frac{\sin (u_{3})]_{0}^{4 π}}{2})$ dan $\frac{16}{16}$ .

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} - (\frac{{u_{2}}^{3}}{3}]_{0}^{0})) + \frac{- \frac{1}{32} (u_{1}]_{0}^{2 π} + \frac{\sin (u_{3})]_{0}^{4 π}}{2}) \cdot 16}{16} + \frac{\sin (u_{1})]_{0}^{2 π}}{16} + \frac{u_{1}}{16}]_{0}^{2 π})$

Langkah 34.4

Gabungkan pembilang dari penyebut persekutuan.

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} - (\frac{{u_{2}}^{3}}{3}]_{0}^{0})) + \frac{- \frac{1}{32} (u_{1}]_{0}^{2 π} + \frac{\sin (u_{3})]_{0}^{4 π}}{2}) \cdot 16 + \sin (u_{1})]_{0}^{2 π}}{16} + \frac{u_{1}}{16}]_{0}^{2 π})$

Langkah 34.5

Kalikan $16$ dengan $- 1$ .

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} - (\frac{{u_{2}}^{3}}{3}]_{0}^{0})) + \frac{- 16 (\frac{1}{32}) (u_{1}]_{0}^{2 π} + \frac{\sin (u_{3})]_{0}^{4 π}}{2}) + \sin (u_{1})]_{0}^{2 π}}{16} + \frac{u_{1}}{16}]_{0}^{2 π})$

Langkah 34.6

Gabungkan $- 16$ dan $\frac{1}{32}$ .

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} - (\frac{{u_{2}}^{3}}{3}]_{0}^{0})) + \frac{\frac{- 16}{32} (u_{1}]_{0}^{2 π} + \frac{\sin (u_{3})]_{0}^{4 π}}{2}) + \sin (u_{1})]_{0}^{2 π}}{16} + \frac{u_{1}}{16}]_{0}^{2 π})$

Langkah 34.7

Hapus faktor persekutuan dari $- 16$ dan $32$ .

Ketuk untuk lebih banyak langkah...

Langkah 34.7.1

Faktorkan $16$ dari $- 16$ .

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} - (\frac{{u_{2}}^{3}}{3}]_{0}^{0})) + \frac{\frac{16 (- 1)}{32} (u_{1}]_{0}^{2 π} + \frac{\sin (u_{3})]_{0}^{4 π}}{2}) + \sin (u_{1})]_{0}^{2 π}}{16} + \frac{u_{1}}{16}]_{0}^{2 π})$

Langkah 34.7.2

Batalkan faktor persekutuan.

Ketuk untuk lebih banyak langkah...

Langkah 34.7.2.1

Faktorkan $16$ dari $32$ .

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} - (\frac{{u_{2}}^{3}}{3}]_{0}^{0})) + \frac{\frac{16 \cdot - 1}{16 \cdot 2} (u_{1}]_{0}^{2 π} + \frac{\sin (u_{3})]_{0}^{4 π}}{2}) + \sin (u_{1})]_{0}^{2 π}}{16} + \frac{u_{1}}{16}]_{0}^{2 π})$

Langkah 34.7.2.2

Batalkan faktor persekutuan.

Langkah 34.7.2.3

Tulis kembali pernyataannya.

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} - (\frac{{u_{2}}^{3}}{3}]_{0}^{0})) + \frac{\frac{- 1}{2} (u_{1}]_{0}^{2 π} + \frac{\sin (u_{3})]_{0}^{4 π}}{2}) + \sin (u_{1})]_{0}^{2 π}}{16} + \frac{u_{1}}{16}]_{0}^{2 π})$

Langkah 34.8

Pindahkan tanda negatif di depan pecahan.

$5 (- \frac{1}{16} (u_{2}]_{0}^{0} - (\frac{{u_{2}}^{3}}{3}]_{0}^{0})) + \frac{- \frac{1}{2} (u_{1}]_{0}^{2 π} + \frac{\sin (u_{3})]_{0}^{4 π}}{2}) + \sin (u_{1})]_{0}^{2 π}}{16} + \frac{u_{1}}{16}]_{0}^{2 π})$

Langkah 35

Substitusikan dan sederhanakan.

Ketuk untuk lebih banyak langkah...

Langkah 35.1

Evaluasi $u_{2}$ pada $0$ dan pada $0$ .

$5 (- \frac{1}{16} ((0) + 0 - (\frac{{u_{2}}^{3}}{3}]_{0}^{0})) + \frac{- \frac{1}{2} (u_{1}]_{0}^{2 π} + \frac{\sin (u_{3})]_{0}^{4 π}}{2}) + \sin (u_{1})]_{0}^{2 π}}{16} + \frac{u_{1}}{16}]_{0}^{2 π})$

Langkah 35.2

Evaluasi $\frac{{u_{2}}^{3}}{3}$ pada $0$ dan pada $0$ .

$5 (- \frac{1}{16} ((0) + 0 - ((\frac{0^{3}}{3}) - \frac{0^{3}}{3})) + \frac{- \frac{1}{2} (u_{1}]_{0}^{2 π} + \frac{\sin (u_{3})]_{0}^{4 π}}{2}) + \sin (u_{1})]_{0}^{2 π}}{16} + \frac{u_{1}}{16}]_{0}^{2 π})$

Langkah 35.3

Evaluasi $u_{1}$ pada $2 π$ dan pada $0$ .

$5 (- \frac{1}{16} ((0) + 0 - ((\frac{0^{3}}{3}) - \frac{0^{3}}{3})) + \frac{- \frac{1}{2} ((2 π) + 0 + \frac{\sin (u_{3})]_{0}^{4 π}}{2}) + \sin (u_{1})]_{0}^{2 π}}{16} + \frac{u_{1}}{16}]_{0}^{2 π})$

Langkah 35.4

Evaluasi $\sin (u_{3})$ pada $4 π$ dan pada $0$ .

$5 (- \frac{1}{16} ((0) + 0 - ((\frac{0^{3}}{3}) - \frac{0^{3}}{3})) + \frac{- \frac{1}{2} ((2 π) + 0 + \frac{(\sin (4 π)) - \sin (0)}{2}) + \sin (u_{1})]_{0}^{2 π}}{16} + \frac{u_{1}}{16}]_{0}^{2 π})$

Langkah 35.5

Evaluasi $\sin (u_{1})$ pada $2 π$ dan pada $0$ .

$5 (- \frac{1}{16} ((0) + 0 - ((\frac{0^{3}}{3}) - \frac{0^{3}}{3})) + \frac{- \frac{1}{2} ((2 π) + 0 + \frac{(\sin (4 π)) - \sin (0)}{2}) + (\sin (2 π)) - \sin (0)}{16} + \frac{u_{1}}{16}]_{0}^{2 π})$

Langkah 35.6

Evaluasi $\frac{u_{1}}{16}$ pada $2 π$ dan pada $0$ .

$5 (- \frac{1}{16} ((0) + 0 - ((\frac{0^{3}}{3}) - \frac{0^{3}}{3})) + \frac{- \frac{1}{2} ((2 π) + 0 + \frac{(\sin (4 π)) - \sin (0)}{2}) + (\sin (2 π)) - \sin (0)}{16} + (\frac{2 π}{16}) - \frac{0}{16})$

Langkah 35.7

Sederhanakan.

Ketuk untuk lebih banyak langkah...

Langkah 35.7.1

Tambahkan $0$ dan $0$ .

$5 (- \frac{1}{16} (0 - ((\frac{0^{3}}{3}) - \frac{0^{3}}{3})) + \frac{- \frac{1}{2} ((2 π) + 0 + \frac{(\sin (4 π)) - \sin (0)}{2}) + (\sin (2 π)) - \sin (0)}{16} + (\frac{2 π}{16}) - \frac{0}{16})$

Langkah 35.7.2

Menaikkan $0$ ke sebarang pangkat positif menghasilkan $0$ .

$5 (- \frac{1}{16} (0 - (\frac{0}{3} - \frac{0^{3}}{3})) + \frac{- \frac{1}{2} ((2 π) + 0 + \frac{(\sin (4 π)) - \sin (0)}{2}) + (\sin (2 π)) - \sin (0)}{16} + (\frac{2 π}{16}) - \frac{0}{16})$

Langkah 35.7.3

Hapus faktor persekutuan dari $0$ dan $3$ .

Ketuk untuk lebih banyak langkah...

Langkah 35.7.3.1

Faktorkan $3$ dari $0$ .

$5 (- \frac{1}{16} (0 - (\frac{3 (0)}{3} - \frac{0^{3}}{3})) + \frac{- \frac{1}{2} ((2 π) + 0 + \frac{(\sin (4 π)) - \sin (0)}{2}) + (\sin (2 π)) - \sin (0)}{16} + (\frac{2 π}{16}) - \frac{0}{16})$

Langkah 35.7.3.2

Batalkan faktor persekutuan.

Ketuk untuk lebih banyak langkah...

Langkah 35.7.3.2.1

Faktorkan $3$ dari $3$ .

$5 (- \frac{1}{16} (0 - (\frac{3 \cdot 0}{3 \cdot 1} - \frac{0^{3}}{3})) + \frac{- \frac{1}{2} ((2 π) + 0 + \frac{(\sin (4 π)) - \sin (0)}{2}) + (\sin (2 π)) - \sin (0)}{16} + (\frac{2 π}{16}) - \frac{0}{16})$

Langkah 35.7.3.2.2

Batalkan faktor persekutuan.

Langkah 35.7.3.2.3

Tulis kembali pernyataannya.

$5 (- \frac{1}{16} (0 - (\frac{0}{1} - \frac{0^{3}}{3})) + \frac{- \frac{1}{2} ((2 π) + 0 + \frac{(\sin (4 π)) - \sin (0)}{2}) + (\sin (2 π)) - \sin (0)}{16} + (\frac{2 π}{16}) - \frac{0}{16})$

Langkah 35.7.3.2.4

Bagilah $0$ dengan $1$ .

$5 (- \frac{1}{16} (0 - (0 - \frac{0^{3}}{3})) + \frac{- \frac{1}{2} ((2 π) + 0 + \frac{(\sin (4 π)) - \sin (0)}{2}) + (\sin (2 π)) - \sin (0)}{16} + (\frac{2 π}{16}) - \frac{0}{16})$

Langkah 35.7.4

Menaikkan $0$ ke sebarang pangkat positif menghasilkan $0$ .

$5 (- \frac{1}{16} (0 - (0 - \frac{0}{3})) + \frac{- \frac{1}{2} ((2 π) + 0 + \frac{(\sin (4 π)) - \sin (0)}{2}) + (\sin (2 π)) - \sin (0)}{16} + (\frac{2 π}{16}) - \frac{0}{16})$

Langkah 35.7.5

Hapus faktor persekutuan dari $0$ dan $3$ .

Ketuk untuk lebih banyak langkah...

Langkah 35.7.5.1

Faktorkan $3$ dari $0$ .

$5 (- \frac{1}{16} (0 - (0 - \frac{3 (0)}{3})) + \frac{- \frac{1}{2} ((2 π) + 0 + \frac{(\sin (4 π)) - \sin (0)}{2}) + (\sin (2 π)) - \sin (0)}{16} + (\frac{2 π}{16}) - \frac{0}{16})$

Langkah 35.7.5.2

Batalkan faktor persekutuan.

Ketuk untuk lebih banyak langkah...

Langkah 35.7.5.2.1

Faktorkan $3$ dari $3$ .

$5 (- \frac{1}{16} (0 - (0 - \frac{3 \cdot 0}{3 \cdot 1})) + \frac{- \frac{1}{2} ((2 π) + 0 + \frac{(\sin (4 π)) - \sin (0)}{2}) + (\sin (2 π)) - \sin (0)}{16} + (\frac{2 π}{16}) - \frac{0}{16})$

Langkah 35.7.5.2.2

Batalkan faktor persekutuan.

$5 (- \frac{1}{16} (0 - (0 - \frac{3 \cdot 0}{3 \cdot 1})) + \frac{- \frac{1}{2} ((2 π) + 0 + \frac{(\sin (4 π)) - \sin (0)}{2}) + (\sin (2 π)) - \sin (0)}{16} + (\frac{2 π}{16}) - \frac{0}{16})$

Langkah 35.7.5.2.3

Tulis kembali pernyataannya.

$5 (- \frac{1}{16} (0 - (0 - \frac{0}{1})) + \frac{- \frac{1}{2} ((2 π) + 0 + \frac{(\sin (4 π)) - \sin (0)}{2}) + (\sin (2 π)) - \sin (0)}{16} + (\frac{2 π}{16}) - \frac{0}{16})$

Langkah 35.7.5.2.4

Bagilah $0$ dengan $1$ .

$5 (- \frac{1}{16} (0 - (0 - 0)) + \frac{- \frac{1}{2} ((2 π) + 0 + \frac{(\sin (4 π)) - \sin (0)}{2}) + (\sin (2 π)) - \sin (0)}{16} + (\frac{2 π}{16}) - \frac{0}{16})$

Langkah 35.7.6

Kalikan $- 1$ dengan $0$ .

$5 (- \frac{1}{16} (0 - (0 + 0)) + \frac{- \frac{1}{2} ((2 π) + 0 + \frac{(\sin (4 π)) - \sin (0)}{2}) + (\sin (2 π)) - \sin (0)}{16} + (\frac{2 π}{16}) - \frac{0}{16})$

Langkah 35.7.7

Tambahkan $0$ dan $0$ .

$5 (- \frac{1}{16} (0 - 0) + \frac{- \frac{1}{2} ((2 π) + 0 + \frac{(\sin (4 π)) - \sin (0)}{2}) + (\sin (2 π)) - \sin (0)}{16} + (\frac{2 π}{16}) - \frac{0}{16})$

Langkah 35.7.8

Kalikan $- 1$ dengan $0$ .

$5 (- \frac{1}{16} (0 + 0) + \frac{- \frac{1}{2} ((2 π) + 0 + \frac{(\sin (4 π)) - \sin (0)}{2}) + (\sin (2 π)) - \sin (0)}{16} + (\frac{2 π}{16}) - \frac{0}{16})$

Langkah 35.7.9

Tambahkan $0$ dan $0$ .

$5 (- \frac{1}{16} \cdot 0 + \frac{- \frac{1}{2} ((2 π) + 0 + \frac{(\sin (4 π)) - \sin (0)}{2}) + (\sin (2 π)) - \sin (0)}{16} + (\frac{2 π}{16}) - \frac{0}{16})$

Langkah 35.7.10

Kalikan $0$ dengan $- 1$ .

$5 (0 (\frac{1}{16}) + \frac{- \frac{1}{2} ((2 π) + 0 + \frac{(\sin (4 π)) - \sin (0)}{2}) + (\sin (2 π)) - \sin (0)}{16} + (\frac{2 π}{16}) - \frac{0}{16})$

Langkah 35.7.11

Kalikan $0$ dengan $\frac{1}{16}$ .

$5 (0 + \frac{- \frac{1}{2} ((2 π) + 0 + \frac{(\sin (4 π)) - \sin (0)}{2}) + (\sin (2 π)) - \sin (0)}{16} + (\frac{2 π}{16}) - \frac{0}{16})$

Langkah 35.7.12

Tambahkan $2 π$ dan $0$ .

$5 (0 + \frac{- \frac{1}{2} (2 π + \frac{(\sin (4 π)) - \sin (0)}{2}) + (\sin (2 π)) - \sin (0)}{16} + (\frac{2 π}{16}) - \frac{0}{16})$

Langkah 35.7.13

Kurangi $- \frac{- \frac{1}{2} (2 π + \frac{\sin (4 π) - \sin (0)}{2}) + \sin (2 π) - \sin (0)}{16}$ dengan $0$ .

$5 (\frac{- \frac{1}{2} (2 π + \frac{\sin (4 π) - \sin (0)}{2}) + \sin (2 π) - \sin (0)}{16} + (\frac{2 π}{16}) - \frac{0}{16})$

Langkah 35.7.14

Hapus faktor persekutuan dari $2$ dan $16$ .

Ketuk untuk lebih banyak langkah...

Langkah 35.7.14.1

Faktorkan $2$ dari $2 π$ .

$5 (\frac{- \frac{1}{2} (2 π + \frac{\sin (4 π) - \sin (0)}{2}) + \sin (2 π) - \sin (0)}{16} + \frac{2 (π)}{16} - \frac{0}{16})$

Langkah 35.7.14.2

Batalkan faktor persekutuan.

Ketuk untuk lebih banyak langkah...

Langkah 35.7.14.2.1

Faktorkan $2$ dari $16$ .

$5 (\frac{- \frac{1}{2} (2 π + \frac{\sin (4 π) - \sin (0)}{2}) + \sin (2 π) - \sin (0)}{16} + \frac{2 π}{2 \cdot 8} - \frac{0}{16})$

Langkah 35.7.14.2.2

Batalkan faktor persekutuan.

$5 (\frac{- \frac{1}{2} (2 π + \frac{\sin (4 π) - \sin (0)}{2}) + \sin (2 π) - \sin (0)}{16} + \frac{2 π}{2 \cdot 8} - \frac{0}{16})$

Langkah 35.7.14.2.3

Tulis kembali pernyataannya.

$5 (\frac{- \frac{1}{2} (2 π + \frac{\sin (4 π) - \sin (0)}{2}) + \sin (2 π) - \sin (0)}{16} + \frac{π}{8} - \frac{0}{16})$

Langkah 35.7.15

Hapus faktor persekutuan dari $0$ dan $16$ .

Ketuk untuk lebih banyak langkah...

Langkah 35.7.15.1

Faktorkan $16$ dari $0$ .

$5 (\frac{- \frac{1}{2} (2 π + \frac{\sin (4 π) - \sin (0)}{2}) + \sin (2 π) - \sin (0)}{16} + \frac{π}{8} - \frac{16 (0)}{16})$

Langkah 35.7.15.2

Batalkan faktor persekutuan.

Ketuk untuk lebih banyak langkah...

Langkah 35.7.15.2.1

Faktorkan $16$ dari $16$ .

$5 (\frac{- \frac{1}{2} (2 π + \frac{\sin (4 π) - \sin (0)}{2}) + \sin (2 π) - \sin (0)}{16} + \frac{π}{8} - \frac{16 \cdot 0}{16 \cdot 1})$

Langkah 35.7.15.2.2

Batalkan faktor persekutuan.

$5 (\frac{- \frac{1}{2} (2 π + \frac{\sin (4 π) - \sin (0)}{2}) + \sin (2 π) - \sin (0)}{16} + \frac{π}{8} - \frac{16 \cdot 0}{16 \cdot 1})$

Langkah 35.7.15.2.3

Tulis kembali pernyataannya.

$5 (\frac{- \frac{1}{2} (2 π + \frac{\sin (4 π) - \sin (0)}{2}) + \sin (2 π) - \sin (0)}{16} + \frac{π}{8} - \frac{0}{1})$

Langkah 35.7.15.2.4

Bagilah $0$ dengan $1$ .

$5 (\frac{- \frac{1}{2} (2 π + \frac{\sin (4 π) - \sin (0)}{2}) + \sin (2 π) - \sin (0)}{16} + \frac{π}{8} - 0)$

Langkah 35.7.16

Kalikan $- 1$ dengan $0$ .

$5 (\frac{- \frac{1}{2} (2 π + \frac{\sin (4 π) - \sin (0)}{2}) + \sin (2 π) - \sin (0)}{16} + \frac{π}{8} + 0)$

Langkah 35.7.17

Tambahkan $\frac{π}{8}$ dan $0$ .

$5 (\frac{- \frac{1}{2} (2 π + \frac{\sin (4 π) - \sin (0)}{2}) + \sin (2 π) - \sin (0)}{16} + \frac{π}{8})$

Langkah 36

Sederhanakan.

Ketuk untuk lebih banyak langkah...

Langkah 36.1

Nilai eksak dari $\sin (0)$ adalah $0$ .

$5 (\frac{- \frac{1}{2} (2 π + \frac{\sin (4 π) - 0}{2}) + \sin (2 π) - \sin (0)}{16} + \frac{π}{8})$

Langkah 36.2

Nilai eksak dari $\sin (0)$ adalah $0$ .

$5 (\frac{- \frac{1}{2} (2 π + \frac{\sin (4 π) - 0}{2}) + \sin (2 π) - 0}{16} + \frac{π}{8})$

Langkah 36.3

Kalikan $- 1$ dengan $0$ .

$5 (\frac{- \frac{1}{2} (2 π + \frac{\sin (4 π) + 0}{2}) + \sin (2 π) - 0}{16} + \frac{π}{8})$

Langkah 36.4

Tambahkan $\sin (4 π)$ dan $0$ .

$5 (\frac{- \frac{1}{2} (2 π + \frac{\sin (4 π)}{2}) + \sin (2 π) - 0}{16} + \frac{π}{8})$

Langkah 36.5

Kalikan $- 1$ dengan $0$ .

$5 (\frac{- \frac{1}{2} (2 π + \frac{\sin (4 π)}{2}) + \sin (2 π) + 0}{16} + \frac{π}{8})$

Langkah 36.6

Tambahkan $- \frac{1}{2} (2 π + \frac{\sin (4 π)}{2}) + \sin (2 π)$ dan $0$ .

$5 (\frac{- \frac{1}{2} (2 π + \frac{\sin (4 π)}{2}) + \sin (2 π)}{16} + \frac{π}{8})$

Langkah 37

Sederhanakan.

Ketuk untuk lebih banyak langkah...

Langkah 37.1

Sederhanakan setiap suku.

Ketuk untuk lebih banyak langkah...

Langkah 37.1.1

Sederhanakan pembilangnya.

Ketuk untuk lebih banyak langkah...

Langkah 37.1.1.1

Kurangi rotasi penuh dari $2 π$ sampai sudutnya lebih besar dari atau sama dengan $0$ dan lebih kecil dari $2 π$ .

$5 (\frac{- \frac{1}{2} (2 π + \frac{\sin (0)}{2}) + \sin (2 π)}{16} + \frac{π}{8})$

Langkah 37.1.1.2

Nilai eksak dari $\sin (0)$ adalah $0$ .

$5 (\frac{- \frac{1}{2} (2 π + \frac{0}{2}) + \sin (2 π)}{16} + \frac{π}{8})$

Langkah 37.1.2

Bagilah $0$ dengan $2$ .

$5 (\frac{- \frac{1}{2} (2 π + 0) + \sin (2 π)}{16} + \frac{π}{8})$

Langkah 37.2

Tambahkan $2 π$ dan $0$ .

$5 (\frac{- \frac{1}{2} (2 π) + \sin (2 π)}{16} + \frac{π}{8})$

Langkah 37.3

Batalkan faktor persekutuan dari $2$ .

Ketuk untuk lebih banyak langkah...

Langkah 37.3.1

Pindahkan negatif pertama pada $- \frac{1}{2}$ ke dalam pembilangnya.

$5 (\frac{\frac{- 1}{2} (2 π) + \sin (2 π)}{16} + \frac{π}{8})$

Langkah 37.3.2

Faktorkan $2$ dari $2 π$ .

$5 (\frac{\frac{- 1}{2} (2 (π)) + \sin (2 π)}{16} + \frac{π}{8})$

Langkah 37.3.3

Batalkan faktor persekutuan.

$5 (\frac{\frac{- 1}{2} (2 π) + \sin (2 π)}{16} + \frac{π}{8})$

Langkah 37.3.4

Tulis kembali pernyataannya.

$5 (\frac{- π + \sin (2 π)}{16} + \frac{π}{8})$

Langkah 37.4

Sederhanakan setiap suku.

Ketuk untuk lebih banyak langkah...

Langkah 37.4.1

Sederhanakan pembilangnya.

Ketuk untuk lebih banyak langkah...

Langkah 37.4.1.1

Kurangi rotasi penuh dari $2 π$ sampai sudutnya lebih besar dari atau sama dengan $0$ dan lebih kecil dari $2 π$ .

$5 (\frac{- π + \sin (0)}{16} + \frac{π}{8})$

Langkah 37.4.1.2

Nilai eksak dari $\sin (0)$ adalah $0$ .

$5 (\frac{- π + 0}{16} + \frac{π}{8})$

Langkah 37.4.1.3

Tambahkan $- π$ dan $0$ .

$5 (\frac{- π}{16} + \frac{π}{8})$

Langkah 37.4.2

Pindahkan tanda negatif di depan pecahan.

$5 (- \frac{π}{16} + \frac{π}{8})$

Langkah 37.5

Untuk menuliskan $\frac{π}{8}$ sebagai pecahan dengan penyebut umum, kalikan dengan $\frac{2}{2}$ .

$5 (- \frac{π}{16} + \frac{π}{8} \cdot \frac{2}{2})$

Langkah 37.6

Tulis setiap pernyataan menggunakan penyebut umum dari $16$ , dengan mengalikan masing-masing pembilang dan penyebut dengan faktor dari $1$ yang sesuai.

Ketuk untuk lebih banyak langkah...

Langkah 37.6.1

Kalikan $\frac{π}{8}$ dengan $\frac{2}{2}$ .

$5 (- \frac{π}{16} + \frac{π \cdot 2}{8 \cdot 2})$

Langkah 37.6.2

Kalikan $8$ dengan $2$ .

$5 (- \frac{π}{16} + \frac{π \cdot 2}{16})$

Langkah 37.7

Gabungkan pembilang dari penyebut persekutuan.

$5 \frac{- π + π \cdot 2}{16}$

Langkah 37.8

Pindahkan $2$ ke sebelah kiri $π$ .

$5 \frac{- π + 2 \cdot π}{16}$

Langkah 37.9

Tambahkan $- π$ dan $2 π$ .

$5 \frac{π}{16}$

Langkah 37.10

Gabungkan $5$ dan $\frac{π}{16}$ .

$\frac{5 π}{16}$

Langkah 38

Hasilnya dapat ditampilkan dalam beberapa bentuk.

Bentuk Eksak:

$\frac{5 π}{16}$

Bentuk Desimal:

$0.98174770 \dots$