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Math Help - integration problem!

  1. #1
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    integration problem!

    what is the integral of x/(x^3 -1)

    i got an answer of ln(x-1)/3 - ln(2((x^2 + x + 1)^(1/2))/(3)^(1/2)) + ((3)^(1/2))arctan(2(x+(1/2))/((3)^(1/2))) + C
    but im not sure if thats at all right..

    any help would be appreciated
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  2. #2
    MHF Contributor red_dog's Avatar
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    \frac{x}{x^3-1}=\frac{x}{(x-1)(x^2+x+1)}=\frac{A}{x-1}+\frac{Bx+C}{x^2+x+1}

    x=(A+B)x^2+(A-B+C)x+A-C\Rightarrow\left\{\begin{array}{lll}A+B=0\\A-B+C=1\\A-C=0\end{array}\right.

    Now find A, B, C.
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