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

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

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Answer 1 · 2016-12-20T13:47:43

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.

$\int x^{2} csc x d x = 2 i x (L i_{2} (- e^{i x}) - L i_{2} (e^{i x})) + 2 (L i_{3} (e^{i x}) - L i_{3} (e^{- i x})) + x^{2} (ln (1 - e^{i} x) - ln (1 + e^{i x}))$ $int x^2cscx dx = 2ix(Li_2(-e^(ix)) - Li_2(e^(ix))) + 2(Li_3(e^(ix))-Li_3(e^(-ix)))+x^2(ln(1-e^ix)-ln(1+e^(ix)))$

$L i_{n} (x)$ $Li_n(x)$ is the polylogarithm function (No. I cannot explain that.)

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

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