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 (10,703)

 +10 Evaluate $\space\lim\limits_{n\to\infty}\sqrt{n}\int\limits_{-\infty}^{+\infty}\frac{\cos t}{\left(1+t^2\right)^n}dt$ +10 How to evaluate $\int_0^\pi(\ln(\sin(x)))^2 \, dx$ +10 Analytical approximation of integral of Bessel function +10 Proving $\left(1-\frac13+\frac15-\frac17+\cdots\right)^2=\frac38\left(\frac1{1^2}+\frac1{2^2}+\frac1{3^2}+\frac1{4^2}+\cdots\right)$

### 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 $k$)?

### Tags (109)

 501 integration × 152 95 improper-integrals × 28 278 definite-integrals × 65 87 complex-analysis × 37 261 calculus × 70 83 closed-form × 14 144 sequences-and-series × 29 81 limits × 20 113 real-analysis × 29 56 gamma-function × 11

### Accounts (4)

 Mathematics 10,703 rep 12045 Stack Overflow 113 rep 4 Physics 101 rep 2 Area 51 101 rep 1