Mathematics
Olivier Oloa's user avatar
Olivier Oloa's user avatar
Olivier Oloa's user avatar
Olivier Oloa
  • Member for 9 years, 5 months
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  • France
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A popular integral on MSE that resisted numerous efforts for more than two years, here is a possible approach.

An integral expressed in terms of a nice logarithmic series.

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237
Evaluate $ \int_{0}^{\frac{\pi}2}\frac1{(1+x^2)(1+\tan x)}\:\mathrm dx$
82
Ramanujan log-trigonometric integrals
82
A strange integral: $\int_{-\infty}^{+\infty} {dx \over 1 + \left(x + \tan x\right)^2} = \pi.$
65
Evaluating $\int_{0}^{1}\cdots\int_{0}^{1}\bigl\{\frac{1}{x_{1}\cdots x_{n}}\bigr\}^{2}\:\mathrm{d}x_{1}\cdots\mathrm{d}x_{n}$
62
How can I prove $\pi=e^{3/2}\prod_{n=2}^{\infty}e\left(1-\frac{1}{n^2}\right)^{n^2}$?

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