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

1 Answer
Jim H
Dec 20, 2016

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.)

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