What is the integral of (x^7)/((5-x^8)^2) ?

The integral of (x^7)/((5-x^8)^2) is 1/(8(5-x^8))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (x^7)/((5-x^8)^2)

\int \frac{x ^{7}}{( 5 - x ^{8} ) ^{2}} d x

\frac{1}{8 ( 5 - x ^{8} )} + C

Solution steps

\int \frac{x ^{7}}{( 5 - x ^{8} ) ^{2}} d x

Apply u-substitution

= \int - \frac{1}{8 u ^{2}} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \frac{1}{8} \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

= - \frac{1}{8} (- \frac{1}{u})

Substitute back

u = 5 - x^{8}

= - \frac{1}{8} (- \frac{1}{5 - x ^{8}})

Simplify

- \frac{1}{8} (- \frac{1}{5 - x ^{8}}) : \frac{1}{8 ( 5 - x ^{8} )}

= \frac{1}{8 ( 5 - x ^{8} )}

Add a constant to the solution

= \frac{1}{8 ( 5 - x ^{8} )} + C

What is the integral of (x^7)/((5-x^8)^2) ?
The integral of (x^7)/((5-x^8)^2) is 1/(8(5-x^8))+C