Question

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

Answer 1

You will need some more advanced mathematics than just integration by parts.

Explanation:

WolframAlpha gives an answer involving complex values functions including the complex valued polylogarithm function.

`int x^2cscx dx = 2ix(Li_2(-e^(ix)) - Li_2(e^(ix))) + 2(Li_3(e^(ix))-Li_3(e^(-ix)))+x^2(ln(1-e^ix)-ln(1+e^(ix)))`

`Li_n(x)` is the polylogarithm function (No. I cannot explain that.)