Prove that: $$\int_{-\infty }^{+\infty }{\frac{{{x}^{4}}\text{d}x}{\left( \beta +{{\text{e}}^{x}} \right)\left( 1-{{\text{e}}^{-x}} \right)}}=\frac{\left( {{\pi }^{2}}+{{\ln }^{2}}\beta \right)}{15\left( \beta +1 \right)}\left( 7{{\pi }^{2}}+3{{\ln }^{2}}\beta \right)\ln \beta,\ \ \beta>0$$
2026-04-19 16:29:18.1776616158
A rational integral with exponential denominator
362 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in CALCULUS
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