What is the integral of \sqrt[6]{cot(x)}csc^2(x) ?

The integral of \sqrt[6]{cot(x)}csc^2(x) is -6/7 cot^{7/6}(x)+C

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integral of \sqrt[6]{cot(x)}csc^2(x)

- \frac{6}{7} cot^{\frac{7}{6}} (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{6}{7} u^{\frac{7}{6}}

= - \frac{6}{7} u^{\frac{7}{6}}

Substitute back

u = cot (x)

= - \frac{6}{7} cot^{\frac{7}{6}} (x)

Add a constant to the solution

= - \frac{6}{7} cot^{\frac{7}{6}} (x) + C

\int_{0}^{1} 1 - x^{2} d x

e^{-, at}

\frac{d}{d θ} (sin (\frac{θ}{2}))

\frac{d y}{d x} = \frac{4 x}{y}, y (2) = - 2

\frac{d}{d x} (\frac{x ^{3} - 3 x ^{2} + 9}{x ^{2}})

What is the integral of \sqrt[6]{cot(x)}csc^2(x) ?
The integral of \sqrt[6]{cot(x)}csc^2(x) is -6/7 cot^{7/6}(x)+C