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mrtaurho's user avatar
mrtaurho's user avatar
mrtaurho
  • Member for 6 years, 3 months
  • Last seen this week
  • Germany
22 votes
Accepted

A Series For the Golden Ratio

15 votes
Accepted

What is the dot in "$1.2.4$"?

15 votes
Accepted

How to find $\int_0^{{\pi}/{2}} (\pi x-4x^2)\log(1+\tan x)\mathrm dx$

13 votes
Accepted

Is $\int\limits_0^\infty\frac{\sin y}{y^{s+1}}dy=-\Gamma(-s)\sin(\frac{\pi s}{2})$ for $\operatorname{Re}(s)\in (-1,0)$ obvious?

12 votes

Can you compute $\int_0^1\frac{\log(x)\log(1-x)}{x}dx$ more precisely than $1.20206$ and do a comparision with $\zeta(3)$?

11 votes
Accepted

Why is Catalan's constant $G$ important?

11 votes
Accepted

Find $\int^{\pi/2}_0 \frac{\sin^{n-2}(x)}{(1+\cos x)^n}\mathrm dx$

11 votes
Accepted

Applications of Ramanujan's Master Theorem

10 votes

Find $x$: $\sqrt[3]{1+\sqrt{x}}+\sqrt[3]{1-\sqrt{x}}=\sqrt[3]{5}$

10 votes
Accepted

Integral $\int_a^\infty \frac{\arctan(x+b)}{x^2+c}dx$

10 votes
Accepted

Integral of $\ln(\tanh(x))$

9 votes
Accepted

How to evaluate $\int_{0}^{2\pi}x^2\ln (1-\cos x)dx$?

8 votes
Accepted

Proving $\Im\operatorname{Li}_2(\sqrt i(\sqrt 2-1))=\frac34G+\frac18\pi\ln(\sqrt2-1)$

8 votes

Solving $\int_0^{\infty} \ln^m(x)\sin\left(x^n\right)\:dx$

8 votes
Accepted

$\int_{0}^{\infty} \frac{1}{1 + x^r}\:dx = \frac{1}{r}\Gamma\left( \frac{r - 1}{r}\right)\Gamma\left( \frac{1}{r}\right)$

8 votes

Show that $\int_0^{\infty}\frac{\operatorname{Li}_s(-x)}{x^{\alpha+1}}\mathrm dx=-\frac1{\alpha^s}\frac{\pi}{\sin(\pi \alpha)}$

8 votes

Show that $\int_{0}^{\pi/4}\int_{0}^{\pi/4}\left(\sec(x+y)+\sec(x-y)\right)\mathrm{d}x\mathrm{d}y=2G$

8 votes

Integral $\int_0^\infty \frac{\ln(1+x+x^2)}{1+x^2}dx$

8 votes

Is $\int_1^\infty\frac{1}{\sqrt{\Gamma(x)}}\mathrm dx$ a rational number?

8 votes

Prove that $\sum\limits_{n=0}^\infty\binom{2n}n\frac n{4^n(n+1)^2}=\ln(16)-2$

8 votes
Accepted

What is the Group of Bijections of the circle

7 votes
Accepted

Show $\int_{0}^{\infty}\frac{dx}{\sqrt{x^{4}+x}} = \frac{2 \Gamma(1/3) \Gamma(7/6)}{\sqrtπ}≈2.80436$

7 votes
Accepted

Evaluate $\int_{0}^{\frac{\pi}{2}} x\ln(\tan(x))dx $

7 votes
Accepted

How to show that $ \prod\limits_{r=1}^{n}\Gamma{ \left({\frac {r}{n+1}}\right)}={\sqrt {\frac {(2\pi )^{n}}{n+1}}}$?

6 votes

How to evaluate this nonelementary integral?

6 votes

Evaluate $\int_{0}^{\frac{\pi}{2}}\frac{x^2}{ \sin x}dx$

6 votes
Accepted

Can someone breakdown (ELI$5$) how an integral of a power is evaluated, please?

6 votes
Accepted

Clarify the usage of symbols for "-morphism".

6 votes

How can I prove $\int_{0}^{1} \frac {x-1}{\log(x) (1+x^3)}dx=\frac {\log3}{2}$

6 votes
Accepted

Find the value of $S_1+S_2$

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