How do you integrate $\int x^{2} cot 2 x d x$ $int x^2 cot2 x dx$ using integration by parts?

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Answer 1 · 2016-03-18T13:54:42

As a first step choose $u = x^{2}$ $u=x^2$ and $d v = cot x d x$ $dv = cotx dx$

This gets us $d u = 2 x d x$ $du=2xdx$ and $v = \frac{1}{2} ln (sin x)$ $v = 1/2ln(sinx)$ ,
so the integral is equal to

$\frac{1}{2} x^{2} ln (sin x) - \int x ln (sin x) d x$ $1/2x^2ln(sinx) - int x ln(sinx) dx$

Writing the integral now will involve the polylogarithmic function. You can read more about that here.

How do you integrate ∫x2cot2xdxint x^2 cot2 x dx using integration by parts?