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Prove that: $$\int_{-\infty }^{+\infty }{\frac{{{x}^{4}}\text{d}x}{\left( \beta +{{\text{e}}^{x}} \right)\left( 1-{{\text{e}}^{-x}} \right)}}=\frac{\left( {{\pi }^{2}}+{{\ln }^{2}}\beta \right)}{15\left( \beta +1 \right)}\left( 7{{\pi }^{2}}+3{{\ln }^{2}}\beta \right)\ln \beta,\ \ \beta>0$$

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I bet it is given $\,\beta > 0\,$ ...? –  DonAntonio Feb 10 '13 at 17:56
Really, if you read through the solution to your other question, you should be able to do this one in principle. –  Ron Gordon Feb 11 '13 at 1:21
@rlgordonma : THx! I am just reading your solution –  gauss115 Feb 11 '13 at 2:26

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