What is the integral of \sqrt[8]{cot(x)}csc^2(x) ?

The integral of \sqrt[8]{cot(x)}csc^2(x) is -8/9 cot^{9/8}(x)+C

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integral of \sqrt[8]{cot(x)}csc^2(x)

- \frac{8}{9} cot^{\frac{9}{8}} (x) + C

Solution steps

Apply u-substitution

Take the constant out:

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

Apply the Power Rule

= - \frac{8}{9} u^{\frac{9}{8}}

Substitute back

u = cot (x)

= - \frac{8}{9} cot^{\frac{9}{8}} (x)

Add a constant to the solution

= - \frac{8}{9} cot^{\frac{9}{8}} (x) + C

What is the integral of \sqrt[8]{cot(x)}csc^2(x) ?
The integral of \sqrt[8]{cot(x)}csc^2(x) is -8/9 cot^{9/8}(x)+C