Question

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

Answer 1

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

Explanation:

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.