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}}

= - \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

\frac{d}{d x} (49 - x^{2} - y^{2})

\frac{d}{d x} (c x)

\int \frac{2}{x ^{3} + 3 x ^{2} + 2 x} d x

\int \frac{1}{a ^{2} u ^{2}} d u

f (x) = x^{2} - 4, (- 3, 5)

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