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

The integral of (x^5)/(sqrt(1-x^6)) is -1/3 sqrt(1-x^6)+C

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

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

- \frac{1}{3} 1 - x^{6} + C

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= - \frac{1}{6} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 1 - x^{6}

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

Simplify

- \frac{1}{6} \cdot 2 (1 - x^{6})^{\frac{1}{2}} : - \frac{1}{3} 1 - x^{6}

= - \frac{1}{3} 1 - x^{6}

Add a constant to the solution

= - \frac{1}{3} 1 - x^{6} + C

\frac{d}{d x} (24 x^{\frac{1}{2}})

\frac{\partial}{\partial y} (x e^{y - z})

\frac{d}{d x} (- e^{- x} - e^{- x} x)

\frac{d y}{d x} = 0.0017 y (900 - y)

cos (e^{- 2 θ^{5}})

What is the integral of (x^5)/(sqrt(1-x^6)) ?
The integral of (x^5)/(sqrt(1-x^6)) is -1/3 sqrt(1-x^6)+C