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David G
Lv 6
David G asked in Science & MathematicsMathematics · 1 decade ago

integral of x cot(x)?

I want to find ∫ x cot(x) dx

I know WHAT the answer is: it is x ln(1 - exp(2 i x)) - i/2 (x² + Li_2(exp(2 i x)))

But HOW do I get there?

Li_2 is the dilogarithm function

1 Answer

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  • Jim
    Lv 5
    1 decade ago
    Favorite Answer

    Write cot(x) = cos(x)/sin(x)

    in terms of exp(ix) then substitute u = exp(ix)

    You should get

    ∫ ln(u) (u^2+1)/u(u^2-1) du

    and take it from there.

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