What is the integral of xcsc^2(x)cot(x) ?

The integral of xcsc^2(x)cot(x) is -1/2 xcsc^2(x)-1/2 cot(x)+C

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integral of xcsc^2(x)cot(x)

\int x csc^{2} (x) cot (x) d x

- \frac{1}{2} x csc^{2} (x) - \frac{1}{2} cot (x) + C

Solution steps

\int x csc^{2} (x) cot (x) d x

Apply Integration By Parts

: - \frac{1}{2} x csc^{2} (x) - \int - \frac{1}{2} csc^{2} (x) d x

= - \frac{1}{2} x csc^{2} (x) - \int - \frac{1}{2} csc^{2} (x) d x

\int - \frac{1}{2} csc^{2} (x) d x = \frac{1}{2} cot (x)

= - \frac{1}{2} x csc^{2} (x) - \frac{1}{2} cot (x)

Add a constant to the solution

= - \frac{1}{2} x csc^{2} (x) - \frac{1}{2} cot (x) + C

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What is the integral of xcsc^2(x)cot(x) ?
The integral of xcsc^2(x)cot(x) is -1/2 xcsc^2(x)-1/2 cot(x)+C