tired

 29 Conjectured value of $\int_{0}^{\infty}\left(\frac{x-1}{\ln^2 x}-\frac{1}{\ln x}\right)\frac{\mathrm{d}x}{x^2+1}$ 21 A golden ratio series from a comic book 21 Intuition behind $(-\frac{1}{2})! = \sqrt{\pi}$ 17 $\sum_{k=2}^{\infty} \left( \frac{1}{k-1} - \frac{1}{k} \right) = 1$ 13 Conjecture : $\int_{0}^{\pi\over 2}\mathrm dt{\ln[2\cos(t)]\over t^2+\ln^2[2\cos(t)]}={\pi\over 4}?$

### Reputation (10,663)

 +10 Very *mathematical* general physics book +10 I want to know another method of integration to compute $\int \frac1{a+b\sin x}\ \mathsf dx$ +10 An integral related to the distance distribution between points inside the unit disk +5 An integral related to the distance distribution between points inside the unit disk

### Questions (10)

 20 Evaluate the double sum $\sum_{m=1}^{\infty}\sum_{n=1}^{m-1}\frac{ 1}{m n\left(m^2-n^2\right)^2}$ 11 Asymptotic evaluation of $\int_0^{\pi/4}\cos(x t^2)\tan^2(t)dt$ 5 Is there a way to calculate $\int \limits_0^1\frac{x^3}{\sqrt{x^2-1}}\frac{1}{1-a^2x^2}\frac{1}{1-b^2x^2}\frac{1}{c-x}\mathrm dx$ 3 An integral related to the distance distribution between points inside the unit disk 3 Where does my counting argument fails (Counting of numbers with freshness $k$)?

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