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

Question

2338 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-20T13:47:43

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

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.)

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