Calculus Examples

$\int {(a x^{2} - b)}^{5} d x$

Step 1

Simplify by multiplying through.

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Step 1.1

Expand ${(a x^{2} - b)}^{5}$ .

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Step 1.1.1

Use the Binomial Theorem.

$\int {(a x^{2})}^{5} + 5 {(a x^{2})}^{4} (- b) + 10 {(a x^{2})}^{3} {(- b)}^{2} + 10 {(a x^{2})}^{2} {(- b)}^{3} + 5 (a x^{2}) {(- b)}^{4} + {(- b)}^{5} d x$

Step 1.1.2

Rewrite the exponentiation as a product.

$\int a x^{2} {(a x^{2})}^{4} + 5 {(a x^{2})}^{4} (- b) + 10 {(a x^{2})}^{3} {(- b)}^{2} + 10 {(a x^{2})}^{2} {(- b)}^{3} + 5 (a x^{2}) {(- b)}^{4} + {(- b)}^{5} d x$

Step 1.1.3

Rewrite the exponentiation as a product.

$\int a x^{2} (a x^{2} {(a x^{2})}^{3}) + 5 {(a x^{2})}^{4} (- b) + 10 {(a x^{2})}^{3} {(- b)}^{2} + 10 {(a x^{2})}^{2} {(- b)}^{3} + 5 (a x^{2}) {(- b)}^{4} + {(- b)}^{5} d x$

Step 1.1.4

Rewrite the exponentiation as a product.

$\int a x^{2} (a x^{2} (a x^{2} {(a x^{2})}^{2})) + 5 {(a x^{2})}^{4} (- b) + 10 {(a x^{2})}^{3} {(- b)}^{2} + 10 {(a x^{2})}^{2} {(- b)}^{3} + 5 (a x^{2}) {(- b)}^{4} + {(- b)}^{5} d x$

Step 1.1.5

Rewrite the exponentiation as a product.

$\int a x^{2} (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) + 5 {(a x^{2})}^{4} (- b) + 10 {(a x^{2})}^{3} {(- b)}^{2} + 10 {(a x^{2})}^{2} {(- b)}^{3} + 5 (a x^{2}) {(- b)}^{4} + {(- b)}^{5} d x$

Step 1.1.6

Rewrite the exponentiation as a product.

$\int a x^{2} (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) + 5 (a x^{2} {(a x^{2})}^{3}) (- b) + 10 {(a x^{2})}^{3} {(- b)}^{2} + 10 {(a x^{2})}^{2} {(- b)}^{3} + 5 (a x^{2}) {(- b)}^{4} + {(- b)}^{5} d x$

Step 1.1.7

Rewrite the exponentiation as a product.

$\int a x^{2} (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) + 5 (a x^{2} (a x^{2} {(a x^{2})}^{2})) (- b) + 10 {(a x^{2})}^{3} {(- b)}^{2} + 10 {(a x^{2})}^{2} {(- b)}^{3} + 5 (a x^{2}) {(- b)}^{4} + {(- b)}^{5} d x$

Step 1.1.8

Rewrite the exponentiation as a product.

$\int a x^{2} (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) + 5 (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) (- b) + 10 {(a x^{2})}^{3} {(- b)}^{2} + 10 {(a x^{2})}^{2} {(- b)}^{3} + 5 (a x^{2}) {(- b)}^{4} + {(- b)}^{5} d x$

Step 1.1.9

Rewrite the exponentiation as a product.

$\int a x^{2} (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) + 5 (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) (- b) + 10 (a x^{2} {(a x^{2})}^{2}) {(- b)}^{2} + 10 {(a x^{2})}^{2} {(- b)}^{3} + 5 (a x^{2}) {(- b)}^{4} + {(- b)}^{5} d x$

Step 1.1.10

Rewrite the exponentiation as a product.

$\int a x^{2} (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) + 5 (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) {(- b)}^{2} + 10 {(a x^{2})}^{2} {(- b)}^{3} + 5 (a x^{2}) {(- b)}^{4} + {(- b)}^{5} d x$

Step 1.1.11

Rewrite the exponentiation as a product.

$\int a x^{2} (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) + 5 (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 {(a x^{2})}^{2} {(- b)}^{3} + 5 (a x^{2}) {(- b)}^{4} + {(- b)}^{5} d x$

Step 1.1.12

Rewrite the exponentiation as a product.

$\int a x^{2} (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) + 5 (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) {(- b)}^{3} + 5 (a x^{2}) {(- b)}^{4} + {(- b)}^{5} d x$

Step 1.1.13

Rewrite the exponentiation as a product.

$\int a x^{2} (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) + 5 (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b {(- b)}^{2}) + 5 (a x^{2}) {(- b)}^{4} + {(- b)}^{5} d x$

Step 1.1.14

Rewrite the exponentiation as a product.

$\int a x^{2} (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) + 5 (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) {(- b)}^{4} + {(- b)}^{5} d x$

Step 1.1.15

Rewrite the exponentiation as a product.

Step 1.1.16

Rewrite the exponentiation as a product.

Step 1.1.17

Rewrite the exponentiation as a product.

Step 1.1.18

Rewrite the exponentiation as a product.

Step 1.1.19

Rewrite the exponentiation as a product.

Step 1.1.20

Rewrite the exponentiation as a product.

Step 1.1.21

Rewrite the exponentiation as a product.

Step 1.1.22

Move parentheses.

$\int a x^{2} (a x^{2} (a x^{2} (a x^{2} a) x^{2})) + 5 (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.23

Move parentheses.

$\int a x^{2} (a x^{2} (a x^{2} (a x^{2}) a x^{2})) + 5 (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.24

Move parentheses.

$\int a x^{2} (a x^{2} (a x^{2} a x^{2} a) x^{2}) + 5 (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.25

Move parentheses.

$\int a x^{2} (a x^{2} (a x^{2} a x^{2}) a x^{2}) + 5 (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.26

Move parentheses.

$\int a x^{2} (a x^{2} (a x^{2} a) x^{2} a x^{2}) + 5 (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.27

Move parentheses.

$\int a x^{2} (a x^{2} (a x^{2}) a x^{2} a x^{2}) + 5 (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.28

Move parentheses.

$\int a x^{2} (a x^{2} a x^{2} a x^{2} a) x^{2} + 5 (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.29

Move parentheses.

$\int a x^{2} (a x^{2} a x^{2} a x^{2}) a x^{2} + 5 (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.30

Move parentheses.

$\int a x^{2} (a x^{2} a x^{2} a) x^{2} a x^{2} + 5 (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.31

Move parentheses.

$\int a x^{2} (a x^{2} a x^{2}) a x^{2} a x^{2} + 5 (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.32

Move parentheses.

$\int a x^{2} (a x^{2} a) x^{2} a x^{2} a x^{2} + 5 (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.33

Move parentheses.

$\int a x^{2} (a x^{2}) a x^{2} a x^{2} a x^{2} + 5 (a x^{2} (a x^{2} (a x^{2} (a x^{2})))) (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.34

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 (a x^{2} (a x^{2} (a x^{2} a) x^{2})) (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.35

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 (a x^{2} (a x^{2} (a x^{2}) a x^{2})) (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.36

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 (a x^{2} (a x^{2} a x^{2} a) x^{2}) (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.37

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 (a x^{2} (a x^{2} a x^{2}) a x^{2}) (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.38

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 (a x^{2} (a x^{2} a) x^{2} a x^{2}) (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.39

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 (a x^{2} (a x^{2}) a x^{2} a x^{2}) (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.40

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 (a x^{2} a x^{2} a x^{2} a) x^{2} (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.41

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 (a x^{2} a x^{2} a x^{2}) a x^{2} (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.42

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 (a x^{2} a x^{2} a) x^{2} a x^{2} (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.43

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 (a x^{2} a x^{2}) a x^{2} a x^{2} (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.44

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 (a x^{2} a) x^{2} a x^{2} a x^{2} (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.45

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 (a x^{2}) a x^{2} a x^{2} a x^{2} (- b) + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.46

Move $x^{2}$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 a x^{2} a x^{2} a x^{2} a \cdot - 1 x^{2} b + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.47

Move $a$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 a x^{2} a x^{2} a x^{2} \cdot - 1 a x^{2} b + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.48

Move $x^{2}$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 a x^{2} a x^{2} a \cdot - 1 x^{2} a x^{2} b + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.49

Move $a$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 a x^{2} a x^{2} \cdot - 1 a x^{2} a x^{2} b + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.50

Move $x^{2}$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 a x^{2} a \cdot - 1 x^{2} a x^{2} a x^{2} b + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.51

Move $a$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 a x^{2} \cdot - 1 a x^{2} a x^{2} a x^{2} b + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.52

Move $x^{2}$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 a \cdot - 1 x^{2} a x^{2} a x^{2} a x^{2} b + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.53

Move $a$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 (a x^{2} (a x^{2} (a x^{2}))) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.54

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 (a x^{2} (a x^{2} a) x^{2}) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.55

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 (a x^{2} (a x^{2}) a x^{2}) (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.56

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 (a x^{2} a x^{2} a) x^{2} (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.57

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 (a x^{2} a x^{2}) a x^{2} (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.58

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 (a x^{2} a) x^{2} a x^{2} (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.59

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 (a x^{2}) a x^{2} a x^{2} (- b (- b)) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.60

Move $b$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} (- 1 \cdot - 1 b \cdot b) + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.61

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} (- 1 \cdot - 1 b) b + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.62

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} (- 1 \cdot - 1) b \cdot b + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.63

Move $x^{2}$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a \cdot - 1 \cdot - 1 x^{2} b \cdot b + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.64

Move $a$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} \cdot - 1 \cdot - 1 a x^{2} b \cdot b + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.65

Move $x^{2}$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a \cdot - 1 \cdot - 1 x^{2} a x^{2} b \cdot b + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.66

Move $a$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.67

Move $x^{2}$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a \cdot - 1 \cdot - 1 x^{2} a x^{2} a x^{2} b \cdot b + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.68

Move $a$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 (a x^{2} (a x^{2})) (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.69

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 (a x^{2} a) x^{2} (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.70

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 (a x^{2}) a x^{2} (- b (- b (- b))) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.71

Move $b$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 a x^{2} a x^{2} (- b (- 1 \cdot - 1 b \cdot b)) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.72

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 a x^{2} a x^{2} (- b (- 1 \cdot - 1 b) b) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.73

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 a x^{2} a x^{2} (- b (- 1 \cdot - 1) b \cdot b) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.74

Move $b$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 a x^{2} a x^{2} (- 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b) + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.75

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 a x^{2} a x^{2} (- 1 \cdot - 1 \cdot - 1 b \cdot b) b + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.76

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 a x^{2} a x^{2} (- 1 \cdot - 1 \cdot - 1 b) b \cdot b + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.77

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 a x^{2} a x^{2} (- 1 \cdot - 1 \cdot - 1) b \cdot b \cdot b + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.78

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 a x^{2} a x^{2} (- 1 \cdot - 1) \cdot - 1 b \cdot b \cdot b + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.79

Move $x^{2}$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + (10 a x^{2} a (- 1 \cdot - 1)) \cdot - 1 x^{2} b \cdot b \cdot b + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.80

Move $a$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + (10 a x^{2} (- 1 \cdot - 1)) \cdot - 1 a x^{2} b \cdot b \cdot b + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.81

Move $x^{2}$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + (10 a (- 1 \cdot - 1)) \cdot - 1 x^{2} a x^{2} b \cdot b \cdot b + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.82

Move $a$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + (10 (- 1 \cdot - 1)) \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 (a x^{2}) (- b (- b (- b (- b)))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.83

Move $b$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 a x^{2} (- b (- b (- 1 \cdot - 1 b \cdot b))) - b (- b (- b (- b (- b)))) d x$

Step 1.1.84

Move parentheses.

Step 1.1.85

Move parentheses.

Step 1.1.86

Move $b$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 a x^{2} (- b (- 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b)) - b (- b (- b (- b (- b)))) d x$

Step 1.1.87

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 a x^{2} (- b (- 1 \cdot - 1 \cdot - 1 b \cdot b) b) - b (- b (- b (- b (- b)))) d x$

Step 1.1.88

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 a x^{2} (- b (- 1 \cdot - 1 \cdot - 1 b) b \cdot b) - b (- b (- b (- b (- b)))) d x$

Step 1.1.89

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 a x^{2} (- b (- 1 \cdot - 1 \cdot - 1) b \cdot b \cdot b) - b (- b (- b (- b (- b)))) d x$

Step 1.1.90

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 a x^{2} (- b (- 1 \cdot - 1) \cdot - 1 b \cdot b \cdot b) - b (- b (- b (- b (- b)))) d x$

Step 1.1.91

Move $b$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 a x^{2} ((- (- 1 \cdot - 1)) \cdot - 1 b \cdot b \cdot b \cdot b) - b (- b (- b (- b (- b)))) d x$

Step 1.1.92

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 a x^{2} (- - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b) b - b (- b (- b (- b (- b)))) d x$

Step 1.1.93

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 a x^{2} (- - 1 \cdot - 1 \cdot - 1 b \cdot b) b \cdot b - b (- b (- b (- b (- b)))) d x$

Step 1.1.94

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 a x^{2} (- - 1 \cdot - 1 \cdot - 1 b) b \cdot b \cdot b - b (- b (- b (- b (- b)))) d x$

Step 1.1.95

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 a x^{2} (- - 1 \cdot - 1 \cdot - 1) b \cdot b \cdot b \cdot b - b (- b (- b (- b (- b)))) d x$

Step 1.1.96

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 a x^{2} (- - 1 \cdot - 1) \cdot - 1 b \cdot b \cdot b \cdot b - b (- b (- b (- b (- b)))) d x$

Step 1.1.97

Move $x^{2}$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + (5 a (- - 1 \cdot - 1)) \cdot - 1 x^{2} b \cdot b \cdot b \cdot b - b (- b (- b (- b (- b)))) d x$

Step 1.1.98

Move $a$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + (5 (- - 1 \cdot - 1)) \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - b (- b (- b (- b (- b)))) d x$

Step 1.1.99

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 (- - 1) \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - b (- b (- b (- b (- b)))) d x$

Step 1.1.100

Move $b$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - b (- b (- b (- 1 \cdot - 1 b \cdot b))) d x$

Step 1.1.101

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - b (- b (- b (- 1 \cdot - 1 b) b)) d x$

Step 1.1.102

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - b (- b (- b (- 1 \cdot - 1) b \cdot b)) d x$

Step 1.1.103

Move $b$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - b (- b (- 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b)) d x$

Step 1.1.104

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - b (- b (- 1 \cdot - 1 \cdot - 1 b \cdot b) b) d x$

Step 1.1.105

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - b (- b (- 1 \cdot - 1 \cdot - 1 b) b \cdot b) d x$

Step 1.1.106

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - b (- b (- 1 \cdot - 1 \cdot - 1) b \cdot b \cdot b) d x$

Step 1.1.107

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - b (- b (- 1 \cdot - 1) \cdot - 1 b \cdot b \cdot b) d x$

Step 1.1.108

Move $b$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - b ((- (- 1 \cdot - 1)) \cdot - 1 b \cdot b \cdot b \cdot b) d x$

Step 1.1.109

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - b (- - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b) b d x$

Step 1.1.110

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - b (- - 1 \cdot - 1 \cdot - 1 b \cdot b) b \cdot b d x$

Step 1.1.111

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - b (- - 1 \cdot - 1 \cdot - 1 b) b \cdot b \cdot b d x$

Step 1.1.112

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - b (- - 1 \cdot - 1 \cdot - 1) b \cdot b \cdot b \cdot b d x$

Step 1.1.113

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - b (- - 1 \cdot - 1) \cdot - 1 b \cdot b \cdot b \cdot b d x$

Step 1.1.114

Move $b$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b + (- (- - 1 \cdot - 1)) \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.115

Move parentheses.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} + 5 \cdot - 1 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.116

Multiply $5$ by $- 1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.117

Multiply $10$ by $- 1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b - 10 \cdot - 1 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.118

Multiply $- 10$ by $- 1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b \cdot b + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.119

Raise $b$ to the power of $1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} (b^{1} b) + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.120

Raise $b$ to the power of $1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} (b^{1} b^{1}) + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.121

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{1 + 1} + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.122

Add $1$ and $1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} + 10 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.123

Multiply $10$ by $- 1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 \cdot - 1 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.124

Multiply $- 10$ by $- 1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} + 10 \cdot - 1 a x^{2} a x^{2} b \cdot b \cdot b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.125

Multiply $10$ by $- 1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b \cdot b \cdot b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.126

Raise $b$ to the power of $1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} (b^{1} b) b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.127

Raise $b$ to the power of $1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} (b^{1} b^{1}) b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.128

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{1 + 1} b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.129

Add $1$ and $1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{2} b + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.130

Raise $b$ to the power of $1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} (b^{2} b^{1}) + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.131

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{2 + 1} + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.132

Add $2$ and $1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 \cdot - 1 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.133

Multiply $5$ by $- 1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} - 5 \cdot - 1 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.134

Multiply $- 5$ by $- 1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 \cdot - 1 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.135

Multiply $5$ by $- 1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} - 5 \cdot - 1 a x^{2} b \cdot b \cdot b \cdot b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.136

Multiply $- 5$ by $- 1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b \cdot b \cdot b \cdot b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.137

Raise $b$ to the power of $1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} (b^{1} b) b \cdot b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.138

Raise $b$ to the power of $1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} (b^{1} b^{1}) b \cdot b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.139

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{1 + 1} b \cdot b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.140

Add $1$ and $1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{2} b \cdot b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.141

Raise $b$ to the power of $1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} (b^{2} b^{1}) b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.142

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{2 + 1} b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.143

Add $2$ and $1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{3} b - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.144

Raise $b$ to the power of $1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} (b^{3} b^{1}) - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.145

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{3 + 1} - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.146

Add $3$ and $1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} - - 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.147

Multiply $- 1$ by $- 1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} + 1 \cdot - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.148

Multiply $- 1$ by $1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} - 1 \cdot - 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.149

Multiply $- 1$ by $- 1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} + 1 \cdot - 1 b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.150

Multiply $- 1$ by $1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} - b \cdot b \cdot b \cdot b \cdot b d x$

Step 1.1.151

Factor out negative.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} - (b \cdot b) b \cdot b \cdot b d x$

Step 1.1.152

Raise $b$ to the power of $1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} - (b^{1} b) b \cdot b \cdot b d x$

Step 1.1.153

Raise $b$ to the power of $1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} - (b^{1} b^{1}) b \cdot b \cdot b d x$

Step 1.1.154

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} - b^{1 + 1} b \cdot b \cdot b d x$

Step 1.1.155

Add $1$ and $1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} - b^{2} b \cdot b \cdot b d x$

Step 1.1.156

Factor out negative.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} - (b^{2} b) b \cdot b d x$

Step 1.1.157

Raise $b$ to the power of $1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} - (b^{2} b^{1}) b \cdot b d x$

Step 1.1.158

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} - b^{2 + 1} b \cdot b d x$

Step 1.1.159

Add $2$ and $1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} - b^{3} b \cdot b d x$

Step 1.1.160

Factor out negative.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} - (b^{3} b) b d x$

Step 1.1.161

Raise $b$ to the power of $1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} - (b^{3} b^{1}) b d x$

Step 1.1.162

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} - b^{3 + 1} b d x$

Step 1.1.163

Add $3$ and $1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} - b^{4} b d x$

Step 1.1.164

Factor out negative.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} - (b^{4} b) d x$

Step 1.1.165

Raise $b$ to the power of $1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} - (b^{4} b^{1}) d x$

Step 1.1.166

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} - b^{4 + 1} d x$

Step 1.1.167

Add $4$ and $1$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} - b^{5} d x$

Step 1.1.168

Move $5 a x^{2} b^{4}$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} - b^{5} + 5 a x^{2} b^{4} d x$

Step 1.1.169

Move $- 10 a x^{2} a x^{2} b^{3}$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - b^{5} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.1.170

Move $10 a x^{2} a x^{2} a x^{2} b^{2}$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b - b^{5} + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.1.171

Move $- 5 a x^{2} a x^{2} a x^{2} a x^{2} b$ .

$\int a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - b^{5} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.1.172

Reorder $a x^{2} a x^{2} a x^{2} a x^{2} a x^{2}$ and $- b^{5}$ .

$\int - b^{5} + a x^{2} a x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2

Simplify.

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Step 1.2.1

Raise $a$ to the power of $1$ .

$\int - b^{5} + a^{1} a x^{2} x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.2

Raise $a$ to the power of $1$ .

$\int - b^{5} + a^{1} a^{1} x^{2} x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int - b^{5} + a^{1 + 1} x^{2} x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.4

Add $1$ and $1$ .

$\int - b^{5} + a^{2} x^{2} x^{2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.5

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

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Step 1.2.5.1

Move $x^{2}$ .

$\int - b^{5} + a^{2} (x^{2} x^{2}) a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.5.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int - b^{5} + a^{2} x^{2 + 2} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.5.3

Add $2$ and $2$ .

$\int - b^{5} + a^{2} x^{4} a x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.6

Raise $a$ to the power of $1$ .

$\int - b^{5} + a^{1} a^{2} x^{4} x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.7

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int - b^{5} + a^{1 + 2} x^{4} x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.8

Add $1$ and $2$ .

$\int - b^{5} + a^{3} x^{4} x^{2} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.9

Multiply $x^{4}$ by $x^{2}$ by adding the exponents.

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Step 1.2.9.1

Move $x^{2}$ .

$\int - b^{5} + a^{3} (x^{2} x^{4}) a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.9.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int - b^{5} + a^{3} x^{2 + 4} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.9.3

Add $2$ and $4$ .

$\int - b^{5} + a^{3} x^{6} a x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.10

Raise $a$ to the power of $1$ .

$\int - b^{5} + a^{1} a^{3} x^{6} x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.11

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int - b^{5} + a^{1 + 3} x^{6} x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.12

Add $1$ and $3$ .

$\int - b^{5} + a^{4} x^{6} x^{2} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.13

Multiply $x^{6}$ by $x^{2}$ by adding the exponents.

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Step 1.2.13.1

Move $x^{2}$ .

$\int - b^{5} + a^{4} (x^{2} x^{6}) a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.13.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int - b^{5} + a^{4} x^{2 + 6} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.13.3

Add $2$ and $6$ .

$\int - b^{5} + a^{4} x^{8} a x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.14

Raise $a$ to the power of $1$ .

$\int - b^{5} + a^{1} a^{4} x^{8} x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.15

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int - b^{5} + a^{1 + 4} x^{8} x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.16

Add $1$ and $4$ .

$\int - b^{5} + a^{5} x^{8} x^{2} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.17

Multiply $x^{8}$ by $x^{2}$ by adding the exponents.

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Step 1.2.17.1

Move $x^{2}$ .

$\int - b^{5} + a^{5} (x^{2} x^{8}) - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.17.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int - b^{5} + a^{5} x^{2 + 8} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.17.3

Add $2$ and $8$ .

$\int - b^{5} + a^{5} x^{10} - 5 a x^{2} a x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.18

Raise $a$ to the power of $1$ .

$\int - b^{5} + a^{5} x^{10} - 5 (a^{1} a) x^{2} x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.19

Raise $a$ to the power of $1$ .

$\int - b^{5} + a^{5} x^{10} - 5 (a^{1} a^{1}) x^{2} x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.20

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int - b^{5} + a^{5} x^{10} - 5 a^{1 + 1} x^{2} x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.21

Add $1$ and $1$ .

$\int - b^{5} + a^{5} x^{10} - 5 a^{2} x^{2} x^{2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.22

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

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Step 1.2.22.1

Move $x^{2}$ .

$\int - b^{5} + a^{5} x^{10} - 5 a^{2} (x^{2} x^{2}) a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.22.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int - b^{5} + a^{5} x^{10} - 5 a^{2} x^{2 + 2} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.22.3

Add $2$ and $2$ .

$\int - b^{5} + a^{5} x^{10} - 5 a^{2} x^{4} a x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.23

Raise $a$ to the power of $1$ .

$\int - b^{5} + a^{5} x^{10} - 5 (a^{1} a^{2}) x^{4} x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.24

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int - b^{5} + a^{5} x^{10} - 5 a^{1 + 2} x^{4} x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.25

Add $1$ and $2$ .

$\int - b^{5} + a^{5} x^{10} - 5 a^{3} x^{4} x^{2} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.26

Multiply $x^{4}$ by $x^{2}$ by adding the exponents.

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Step 1.2.26.1

Move $x^{2}$ .

$\int - b^{5} + a^{5} x^{10} - 5 a^{3} (x^{2} x^{4}) a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.26.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int - b^{5} + a^{5} x^{10} - 5 a^{3} x^{2 + 4} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.26.3

Add $2$ and $4$ .

$\int - b^{5} + a^{5} x^{10} - 5 a^{3} x^{6} a x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.27

Raise $a$ to the power of $1$ .

$\int - b^{5} + a^{5} x^{10} - 5 (a^{1} a^{3}) x^{6} x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.28

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int - b^{5} + a^{5} x^{10} - 5 a^{1 + 3} x^{6} x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.29

Add $1$ and $3$ .

$\int - b^{5} + a^{5} x^{10} - 5 a^{4} x^{6} x^{2} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.30

Multiply $x^{6}$ by $x^{2}$ by adding the exponents.

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Step 1.2.30.1

Move $x^{2}$ .

$\int - b^{5} + a^{5} x^{10} - 5 a^{4} (x^{2} x^{6}) b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.30.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int - b^{5} + a^{5} x^{10} - 5 a^{4} x^{2 + 6} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.30.3

Add $2$ and $6$ .

$\int - b^{5} + a^{5} x^{10} - 5 a^{4} x^{8} b + 10 a x^{2} a x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.31

Raise $a$ to the power of $1$ .

$\int - b^{5} + a^{5} x^{10} - 5 a^{4} x^{8} b + 10 (a^{1} a) x^{2} x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.32

Raise $a$ to the power of $1$ .

$\int - b^{5} + a^{5} x^{10} - 5 a^{4} x^{8} b + 10 (a^{1} a^{1}) x^{2} x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.33

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int - b^{5} + a^{5} x^{10} - 5 a^{4} x^{8} b + 10 a^{1 + 1} x^{2} x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.34

Add $1$ and $1$ .

$\int - b^{5} + a^{5} x^{10} - 5 a^{4} x^{8} b + 10 a^{2} x^{2} x^{2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.35

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

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Step 1.2.35.1

Move $x^{2}$ .

$\int - b^{5} + a^{5} x^{10} - 5 a^{4} x^{8} b + 10 a^{2} (x^{2} x^{2}) a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.35.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int - b^{5} + a^{5} x^{10} - 5 a^{4} x^{8} b + 10 a^{2} x^{2 + 2} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.35.3

Add $2$ and $2$ .

$\int - b^{5} + a^{5} x^{10} - 5 a^{4} x^{8} b + 10 a^{2} x^{4} a x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.36

Raise $a$ to the power of $1$ .

$\int - b^{5} + a^{5} x^{10} - 5 a^{4} x^{8} b + 10 (a^{1} a^{2}) x^{4} x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.37

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int - b^{5} + a^{5} x^{10} - 5 a^{4} x^{8} b + 10 a^{1 + 2} x^{4} x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.38

Add $1$ and $2$ .

$\int - b^{5} + a^{5} x^{10} - 5 a^{4} x^{8} b + 10 a^{3} x^{4} x^{2} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.39

Multiply $x^{4}$ by $x^{2}$ by adding the exponents.

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Step 1.2.39.1

Move $x^{2}$ .

$\int - b^{5} + a^{5} x^{10} - 5 a^{4} x^{8} b + 10 a^{3} (x^{2} x^{4}) b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.39.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int - b^{5} + a^{5} x^{10} - 5 a^{4} x^{8} b + 10 a^{3} x^{2 + 4} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.39.3

Add $2$ and $4$ .

$\int - b^{5} + a^{5} x^{10} - 5 a^{4} x^{8} b + 10 a^{3} x^{6} b^{2} - 10 a x^{2} a x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.40

Raise $a$ to the power of $1$ .

$\int - b^{5} + a^{5} x^{10} - 5 a^{4} x^{8} b + 10 a^{3} x^{6} b^{2} - 10 (a^{1} a) x^{2} x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.41

Raise $a$ to the power of $1$ .

$\int - b^{5} + a^{5} x^{10} - 5 a^{4} x^{8} b + 10 a^{3} x^{6} b^{2} - 10 (a^{1} a^{1}) x^{2} x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.42

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int - b^{5} + a^{5} x^{10} - 5 a^{4} x^{8} b + 10 a^{3} x^{6} b^{2} - 10 a^{1 + 1} x^{2} x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.43

Add $1$ and $1$ .

$\int - b^{5} + a^{5} x^{10} - 5 a^{4} x^{8} b + 10 a^{3} x^{6} b^{2} - 10 a^{2} x^{2} x^{2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.44

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

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Step 1.2.44.1

Move $x^{2}$ .

$\int - b^{5} + a^{5} x^{10} - 5 a^{4} x^{8} b + 10 a^{3} x^{6} b^{2} - 10 a^{2} (x^{2} x^{2}) b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.44.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int - b^{5} + a^{5} x^{10} - 5 a^{4} x^{8} b + 10 a^{3} x^{6} b^{2} - 10 a^{2} x^{2 + 2} b^{3} + 5 a x^{2} b^{4} d x$

Step 1.2.44.3

Add $2$ and $2$ .

$\int - b^{5} + a^{5} x^{10} - 5 a^{4} x^{8} b + 10 a^{3} x^{6} b^{2} - 10 a^{2} x^{4} b^{3} + 5 a x^{2} b^{4} d x$

Step 2

Split the single integral into multiple integrals.

$\int - b^{5} d x + \int a^{5} x^{10} d x + \int - 5 a^{4} x^{8} b d x + \int 10 a^{3} x^{6} b^{2} d x + \int - 10 a^{2} x^{4} b^{3} d x + \int 5 a x^{2} b^{4} d x$

Step 3

Apply the constant rule.

$- b^{5} x + C + \int a^{5} x^{10} d x + \int - 5 a^{4} x^{8} b d x + \int 10 a^{3} x^{6} b^{2} d x + \int - 10 a^{2} x^{4} b^{3} d x + \int 5 a x^{2} b^{4} d x$

Step 4

Since $a^{5}$ is constant with respect to $x$ , move $a^{5}$ out of the integral.

$- b^{5} x + C + a^{5} \int x^{10} d x + \int - 5 a^{4} x^{8} b d x + \int 10 a^{3} x^{6} b^{2} d x + \int - 10 a^{2} x^{4} b^{3} d x + \int 5 a x^{2} b^{4} d x$

Step 5

By the Power Rule, the integral of $x^{10}$ with respect to $x$ is $\frac{1}{11} x^{11}$ .

$- b^{5} x + C + a^{5} (\frac{1}{11} x^{11} + C) + \int - 5 a^{4} x^{8} b d x + \int 10 a^{3} x^{6} b^{2} d x + \int - 10 a^{2} x^{4} b^{3} d x + \int 5 a x^{2} b^{4} d x$

Step 6

Since $- 5 a^{4} b$ is constant with respect to $x$ , move $- 5 a^{4} b$ out of the integral.

$- b^{5} x + C + a^{5} (\frac{1}{11} x^{11} + C) - 5 a^{4} b \int x^{8} d x + \int 10 a^{3} x^{6} b^{2} d x + \int - 10 a^{2} x^{4} b^{3} d x + \int 5 a x^{2} b^{4} d x$

Step 7

By the Power Rule, the integral of $x^{8}$ with respect to $x$ is $\frac{1}{9} x^{9}$ .

$- b^{5} x + C + a^{5} (\frac{1}{11} x^{11} + C) - 5 a^{4} b (\frac{1}{9} x^{9} + C) + \int 10 a^{3} x^{6} b^{2} d x + \int - 10 a^{2} x^{4} b^{3} d x + \int 5 a x^{2} b^{4} d x$

Step 8

Since $10 a^{3} b^{2}$ is constant with respect to $x$ , move $10 a^{3} b^{2}$ out of the integral.

$- b^{5} x + C + a^{5} (\frac{1}{11} x^{11} + C) - 5 a^{4} b (\frac{1}{9} x^{9} + C) + 10 a^{3} b^{2} \int x^{6} d x + \int - 10 a^{2} x^{4} b^{3} d x + \int 5 a x^{2} b^{4} d x$

Step 9

By the Power Rule, the integral of $x^{6}$ with respect to $x$ is $\frac{1}{7} x^{7}$ .

$- b^{5} x + C + a^{5} (\frac{1}{11} x^{11} + C) - 5 a^{4} b (\frac{1}{9} x^{9} + C) + 10 a^{3} b^{2} (\frac{1}{7} x^{7} + C) + \int - 10 a^{2} x^{4} b^{3} d x + \int 5 a x^{2} b^{4} d x$

Step 10

Since $- 10 a^{2} b^{3}$ is constant with respect to $x$ , move $- 10 a^{2} b^{3}$ out of the integral.

$- b^{5} x + C + a^{5} (\frac{1}{11} x^{11} + C) - 5 a^{4} b (\frac{1}{9} x^{9} + C) + 10 a^{3} b^{2} (\frac{1}{7} x^{7} + C) - 10 a^{2} b^{3} \int x^{4} d x + \int 5 a x^{2} b^{4} d x$

Step 11

By the Power Rule, the integral of $x^{4}$ with respect to $x$ is $\frac{1}{5} x^{5}$ .

$- b^{5} x + C + a^{5} (\frac{1}{11} x^{11} + C) - 5 a^{4} b (\frac{1}{9} x^{9} + C) + 10 a^{3} b^{2} (\frac{1}{7} x^{7} + C) - 10 a^{2} b^{3} (\frac{1}{5} x^{5} + C) + \int 5 a x^{2} b^{4} d x$

Step 12

Since $5 a b^{4}$ is constant with respect to $x$ , move $5 a b^{4}$ out of the integral.

$- b^{5} x + C + a^{5} (\frac{1}{11} x^{11} + C) - 5 a^{4} b (\frac{1}{9} x^{9} + C) + 10 a^{3} b^{2} (\frac{1}{7} x^{7} + C) - 10 a^{2} b^{3} (\frac{1}{5} x^{5} + C) + 5 a b^{4} \int x^{2} d x$

Step 13

By the Power Rule, the integral of $x^{2}$ with respect to $x$ is $\frac{1}{3} x^{3}$ .

$- b^{5} x + C + a^{5} (\frac{1}{11} x^{11} + C) - 5 a^{4} b (\frac{1}{9} x^{9} + C) + 10 a^{3} b^{2} (\frac{1}{7} x^{7} + C) - 10 a^{2} b^{3} (\frac{1}{5} x^{5} + C) + 5 a b^{4} (\frac{1}{3} x^{3} + C)$

Step 14

Simplify.

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Step 14.1

Simplify.

$- b^{5} x + \frac{a^{5} x^{11}}{11} - \frac{5 b a^{4} x^{9}}{9} + \frac{10 b^{2} a^{3} x^{7}}{7} - 2 a^{2} b^{3} x^{5} + 5 a b^{4} (\frac{1}{3} x^{3}) + C$

Step 14.2

Simplify.

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Step 14.2.1

Combine $\frac{1}{3}$ and $x^{3}$ .

$- b^{5} x + \frac{a^{5} x^{11}}{11} - \frac{5 b a^{4} x^{9}}{9} + \frac{10 b^{2} a^{3} x^{7}}{7} - 2 a^{2} b^{3} x^{5} + 5 a b^{4} \frac{x^{3}}{3} + C$

Step 14.2.2

Combine $5$ and $\frac{x^{3}}{3}$ .

$- b^{5} x + \frac{a^{5} x^{11}}{11} - \frac{5 b a^{4} x^{9}}{9} + \frac{10 b^{2} a^{3} x^{7}}{7} - 2 a^{2} b^{3} x^{5} + a b^{4} \frac{5 x^{3}}{3} + C$

Step 14.2.3

Combine $a$ and $\frac{5 x^{3}}{3}$ .

$- b^{5} x + \frac{a^{5} x^{11}}{11} - \frac{5 b a^{4} x^{9}}{9} + \frac{10 b^{2} a^{3} x^{7}}{7} - 2 a^{2} b^{3} x^{5} + b^{4} \frac{a (5 x^{3})}{3} + C$

Step 14.2.4

Combine $b^{4}$ and $\frac{a (5 x^{3})}{3}$ .

$- b^{5} x + \frac{a^{5} x^{11}}{11} - \frac{5 b a^{4} x^{9}}{9} + \frac{10 b^{2} a^{3} x^{7}}{7} - 2 a^{2} b^{3} x^{5} + \frac{b^{4} (a (5 x^{3}))}{3} + C$

Step 14.2.5

Move $5$ to the left of $a$ .

$- b^{5} x + \frac{a^{5} x^{11}}{11} - \frac{5 b a^{4} x^{9}}{9} + \frac{10 b^{2} a^{3} x^{7}}{7} - 2 a^{2} b^{3} x^{5} + \frac{b^{4} (5 \cdot a x^{3})}{3} + C$

Step 14.2.6

Move $5$ to the left of $b^{4}$ .

$- b^{5} x + \frac{a^{5} x^{11}}{11} - \frac{5 b a^{4} x^{9}}{9} + \frac{10 b^{2} a^{3} x^{7}}{7} - 2 a^{2} b^{3} x^{5} + \frac{5 b^{4} a x^{3}}{3} + C$

Step 15

Remove parentheses.

$- b^{5} x + \frac{1}{11} a^{5} x^{11} - \frac{5}{9} b a^{4} x^{9} + \frac{10}{7} b^{2} a^{3} x^{7} - 2 a^{2} b^{3} x^{5} + \frac{5}{3} b^{4} a x^{3} + C$