What is the integral of (x^6)/((8-x^7)^2) ?

The integral of (x^6)/((8-x^7)^2) is 1/(7(8-x^7))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x^6)/((8-x^7)^2)

\int \frac{x ^{6}}{( 8 - x ^{7} ) ^{2}} d x

\frac{1}{7 ( 8 - x ^{7} )} + C

Solution steps

\int \frac{x ^{6}}{( 8 - x ^{7} ) ^{2}} d x

Apply u-substitution

: \int - \frac{1}{7 u ^{2}} d u

= \int - \frac{1}{7 u ^{2}} d u

Take the constant out:

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

= - \frac{1}{7} \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - \frac{1}{7} (- \frac{1}{u})

Substitute back

u = 8 - x^{7}

= - \frac{1}{7} (- \frac{1}{8 - x ^{7}})

Simplify

- \frac{1}{7} (- \frac{1}{8 - x ^{7}}) : \frac{1}{7 ( 8 - x ^{7} )}

= \frac{1}{7 ( 8 - x ^{7} )}

Add a constant to the solution

= \frac{1}{7 ( 8 - x ^{7} )} + C

\frac{1}{x - 1}, 6

x \to 0 lim (\frac{e ^{x} - 1}{18 x})

\frac{x}{2 x + x - 3}

\int (in x)^{2} d x

x \to \infty lim (1 + x)

What is the integral of (x^6)/((8-x^7)^2) ?
The integral of (x^6)/((8-x^7)^2) is 1/(7(8-x^7))+C