How to calculate the improper integral $$\int_{0}^{\infty}\Big(\frac{x}{\mathrm{e}^x-\mathrm{e}^{-x}}-\frac{1}{2}\Big)\frac{\mathrm{d}x}{x^2}$$ Do you have same idea?
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Are you allowed to use complex numbers? – Guy Mar 27 '14 at 15:42
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Here is exactly the same problem. – Mhenni Benghorbal Mar 27 '14 at 15:47
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@MhenniBenghorbal Thank you very much! – Daoyi Peng Mar 27 '14 at 15:52
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@DaoyiPeng: You are very welcome. – Mhenni Benghorbal Mar 27 '14 at 15:53
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@Sabyasachi Of course, How to solve it? – Daoyi Peng Mar 27 '14 at 15:55
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@DaoyiPeng I was wondering about the substitution $z=e^{ix}$, the first term of the integral can be expressed as a hyperbolic sine function, but in any case you already have a lint to the same question. :) – Guy Mar 27 '14 at 15:59