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Math Help - Integral and limit

  1. #1
    Super Member dhiab's Avatar
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    Integral and limit

    1 ) Calculate this integral :
    ( real and >2)
    2 ) Calculate : .
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  2. #2
    Senior Member Spec's Avatar
    Joined
    Aug 2007
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    What have you tried? Integration by parts and partial fraction decomposition will take care of the integral.

    \int \frac{x\ln x}{(x^2-1)^2}dx=-\frac{1}{2}\frac{\ln x}{x^2-1}+\frac{1}{2}\int \frac{1}{x}\frac{1}{x^2-1}dx

    \frac{1}{x}\frac{1}{x^2-1}=\frac{x}{x^2-1}-\frac{1}{x}
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