Calculus Examples

$\int (x^{1.3} + 7 x^{2.5}) d x$

Step 1

Remove parentheses.

$\int x^{1.3} + 7 x^{2.5} d x$

Step 2

Split the single integral into multiple integrals.

$\int x^{1.3} d x + \int 7 x^{2.5} d x$

Step 3

By the Power Rule, the integral of $x^{1.3}$ with respect to $x$ is $\frac{1}{2.3} x^{2.3}$ .

$\frac{1}{2.3} x^{2.3} + C + \int 7 x^{2.5} d x$

Step 4

Since $7$ is constant with respect to $x$ , move $7$ out of the integral.

$\frac{1}{2.3} x^{2.3} + C + 7 \int x^{2.5} d x$

Step 5

By the Power Rule, the integral of $x^{2.5}$ with respect to $x$ is $\frac{1}{3.5} x^{3.5}$ .

$\frac{1}{2.3} x^{2.3} + C + 7 (\frac{1}{3.5} x^{3.5} + C)$

Step 6

Simplify.

Tap for more steps...

Step 6.1

Simplify.

$0.4347826 x^{2.3} + 7 (\frac{1}{3.5} x^{3.5}) + C$

Step 6.2

Simplify.

Tap for more steps...

Step 6.2.1

Combine $\frac{1}{3.5}$ and $x^{3.5}$ .

$0.4347826 x^{2.3} + 7 \frac{x^{3.5}}{3.5} + C$

Step 6.2.2

Combine $7$ and $\frac{x^{3.5}}{3.5}$ .

$0.4347826 x^{2.3} + \frac{7 x^{3.5}}{3.5} + C$

Step 6.3

Reorder terms.

$0.4347826 x^{2.3} + \frac{7}{3.5} x^{3.5} + C$