What is the integral of \sqrt[11]{cot(x)}csc^2(x) ?

The integral of \sqrt[11]{cot(x)}csc^2(x) is -11/12 cot^{12/11}(x)+C

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integral of \sqrt[11]{cot(x)}csc^2(x)

- \frac{11}{12} cot^{\frac{12}{11}} (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{11}{12} u^{\frac{12}{11}}

= - \frac{11}{12} u^{\frac{12}{11}}

Substitute back

u = cot (x)

= - \frac{11}{12} cot^{\frac{12}{11}} (x)

Add a constant to the solution

= - \frac{11}{12} cot^{\frac{12}{11}} (x) + C

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What is the integral of \sqrt[11]{cot(x)}csc^2(x) ?
The integral of \sqrt[11]{cot(x)}csc^2(x) is -11/12 cot^{12/11}(x)+C