Tagged Questions
8
votes
2answers
72 views
$\int_0^\infty(\log x)^2(\mathrm{sech}\,x)^2\mathrm dx$
Is there any closed-form representation for the following integral?
$$\int_0^\infty(\log x)^2(\mathrm{sech}\,x)^2\mathrm dx,$$
where $\mathrm{sech}\,x$ is the hyperbolic secant, ...
2
votes
1answer
36 views
Evaluation of an integral involving hyperbolic sine and exponential
I am wondering if the following integral can be reduced to either a closed form involving elementary functions, or well-known special functions (such as $\operatorname{erf}$, Bessel functions, etc.):
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5
votes
1answer
81 views
Integral with hyperbolic cosine squared
Does anyone can give me a hint how to integrate the following:
$$\int_0^\infty{\frac{x^2 {\rm d}x}{\mathrm{cosh}^2(x)}}.$$
The answer is $\frac{\pi^2}{12}$ (taken from the book).
I've started with
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