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Olivier Oloa

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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220 Evaluate $ \int_{0}^{\frac{\pi}2}\frac1{(1+x^2)(1+\tan x)}\:\mathrm dx$ Aug 1 '15
76 Ramanujan log-trigonometric integrals Jul 31 '14
76 A strange integral: $\int_{-\infty}^{+\infty} {dx \over 1 + \left(x + \tan x\right)^2} = \pi.$ Nov 10 '14
65 Evaluating $\int_{0}^{1}\cdots\int_{0}^{1}\bigl\{\frac{1}{x_{1}\cdots x_{n}}\bigr\}^{2}\:\mathrm{d}x_{1}\cdots\mathrm{d}x_{n}$ Jul 22 '14
58 How can I prove $\pi=e^{3/2}\prod_{n=2}^{\infty}e\left(1-\frac{1}{n^2}\right)^{n^2}$? Jul 2 '15
58 Closed Form for $~\int_0^1\frac{\text{arctanh }x}{\tan\left(\frac\pi2~x\right)}~dx$ Sep 1 '15
54 Evaluating $\int{ \frac{x^n}{1 + x + \frac{x^2}{2} + \cdots + \frac{x^n}{n!}}}dx$ using Pascal inversion Jun 29 '15
42 How to prove that $\log(x)<x$ when $x>1$? Dec 26 '15
41 Ramanujan log-trigonometric integrals Sep 23 '14
40 Improper Integral $\int_0^1\left(\left\{\frac1x\right\}-\frac12\right)\frac{\log(x)}xdx$ Aug 20 '14
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