How to calculate this integral symbolically?

Asked Oct 03 '17 at 07:50

Active Oct 03 '17 at 07:50

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How to calculate the following integral symbolically with Mathematica:

$$ I = \int_0^\infty \frac{\mathrm{d}x}{(x^2+a^2)(\ln^2x+\pi^2)} $$

where $a>0$ is a real number.

PS: from complex analysis, we can determine it:

$$ I = \frac{2\pi}{(4\ln^2a+\pi^2) \, a} - \frac{1}{a^2+1} $$

asked Oct 03 '17 at 07:50

stone-zeng

1

This seems to be a duplicate of e.g. How to calculate contour integrals with Mathematica? or Paths integrals in the complex plane, unless you show what you have tried. Perhaps there are exact duplicates somewhere on MSE. – Artes Oct 03 '17 at 08:08
The special case $a=1$ cannot be done by Integrate (Mathematica v11.1). So, without providing significant help, it is unlikely it would be able to do it for more general $a$. – QuantumDot Oct 08 '17 at 09:48

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