What is the integral of (x^5)/((1-x^6)^7) ?

The integral of (x^5)/((1-x^6)^7) is 1/(36(1-x^6)^6)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x^5)/((1-x^6)^7)

\int \frac{x ^{5}}{( 1 - x ^{6} ) ^{7}} d x

\frac{1}{36 ( 1 - x ^{6} ) ^{6}} + C

Solution steps

\int \frac{x ^{5}}{( 1 - x ^{6} ) ^{7}} d x

Apply u-substitution

: \int - \frac{1}{6 u ^{7}} d u

= \int - \frac{1}{6 u ^{7}} d u

Take the constant out:

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

= - \frac{1}{6} \cdot \int \frac{1}{u ^{7}} d u

Apply the Power Rule

: - \frac{1}{6 u ^{6}}

= - \frac{1}{6} (- \frac{1}{6 u ^{6}})

Substitute back

u = 1 - x^{6}

= - \frac{1}{6} (- \frac{1}{6 ( 1 - x ^{6} ) ^{6}})

Simplify

- \frac{1}{6} (- \frac{1}{6 ( 1 - x ^{6} ) ^{6}}) : \frac{1}{36 ( 1 - x ^{6} ) ^{6}}

= \frac{1}{36 ( 1 - x ^{6} ) ^{6}}

Add a constant to the solution

= \frac{1}{36 ( 1 - x ^{6} ) ^{6}} + C

\frac{d}{d y} ((y - 12)^{\frac{3}{2}})

\int \frac{2}{3} x^{\frac{3}{2}} - 9 sin (x) + C d x

x \to 1 + lim (ln (x^{2} - 1))

\int x (x - 1) d x

\frac{d ^{2}}{d x ^{2}} ((x^{2} + 6)^{7})

What is the integral of (x^5)/((1-x^6)^7) ?
The integral of (x^5)/((1-x^6)^7) is 1/(36(1-x^6)^6)+C