How do you integrate $int x^2 cot2 x dx$ using integration by parts?

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Answer 1 · 2016-03-18T13:54:42

As a first step choose $u=x^2$ and $dv = cotx dx$

This gets us $du=2xdx$ and $v = 1/2ln(sinx)$ ,
so the integral is equal to

$1/2x^2ln(sinx) - int x ln(sinx) dx$

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

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