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Olivier Oloa's user avatar
Olivier Oloa's user avatar
Olivier Oloa
  • Member for 10 years, 11 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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View all questions and answers
answer
251
Evaluate $\int_{0}^{\frac{\pi}2}\frac1{(1+x^2)(1+\tan x)}\,\Bbb dx$
Aug 1, 2015
answer
86
A strange integral: $\int_{-\infty}^{+\infty} {dx \over 1 + \left(x + \tan x\right)^2} = \pi.$
Nov 10, 2014
question
83
Ramanujan log-trigonometric integrals
Jul 31, 2014
question
67
Evaluating $\int_{0}^{1}\cdots\int_{0}^{1}\bigl\{\frac{1}{x_{1}\cdots x_{n}}\bigr\}^{2}\:\mathrm{d}x_{1}\cdots\mathrm{d}x_{n}$
Jul 22, 2014
answer
63
How can I prove $\pi=e^{3/2}\prod_{n=2}^{\infty}e\left(1-\frac{1}{n^2}\right)^{n^2}$?
Jul 2, 2015
answer
62
Closed Form for $~\int_0^1\frac{\text{arctanh }x}{\tan\left(\frac\pi2~x\right)}~dx$
Sep 1, 2015
answer
53
Evaluating $\int{ \frac{x^n}{1 + x + \frac{x^2}{2} + \cdots + \frac{x^n}{n!}}}dx$ using Pascal inversion
Jun 29, 2015
answer
48
When the integral of products is the product of integrals.
Apr 25, 2017
answer
48
How to prove that $\log(x)<x$ when $x>1$?
Dec 26, 2015
answer
46
Ramanujan log-trigonometric integrals
Sep 23, 2014