What is the integral of (x^5)/((2-x^6)^2) ?

The integral of (x^5)/((2-x^6)^2) is 1/(6(2-x^6))+C

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integral of (x^5)/((2-x^6)^2)

\int \frac{x ^{5}}{( 2 - x ^{6} ) ^{2}} d x

\frac{1}{6 ( 2 - x ^{6} )} + C

Solution steps

\int \frac{x ^{5}}{( 2 - x ^{6} ) ^{2}} d x

Apply u-substitution

: \int - \frac{1}{6 u ^{2}} d u

= \int - \frac{1}{6 u ^{2}} 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 ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

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

Substitute back

u = 2 - x^{6}

= - \frac{1}{6} (- \frac{1}{2 - x ^{6}})

Simplify

- \frac{1}{6} (- \frac{1}{2 - x ^{6}}) : \frac{1}{6 ( 2 - x ^{6} )}

= \frac{1}{6 ( 2 - x ^{6} )}

Add a constant to the solution

= \frac{1}{6 ( 2 - x ^{6} )} + C

\frac{\partial}{\partial x} (2 y - 1)

n \to \infty lim (\frac{( cos ( \frac{1}{n} ) - 1 )}{\frac{1}{n}})

\int - 5 t d t

\frac{d}{d x} (\frac{1 - 2 x}{3 + x})

\frac{d}{d x} (cos (x^{5}))

What is the integral of (x^5)/((2-x^6)^2) ?
The integral of (x^5)/((2-x^6)^2) is 1/(6(2-x^6))+C