Kemono Chen

### Questions (64)

 25 Evaluating $\int_0^1\ln(1+x^2)\ln(x^2+x^3)\frac{dx}{1+x^2}$ 20 Evaluate $\lim\limits_{x\to\infty}\frac1x\int_0^x\max\{\sin t,\sin(t\sqrt2)\}dt$ 18 Evaluating $\int_0^1\frac{x^{2/3}(1-x)^{-1/3}}{1-x+x^2}dx$ 15 Evaluate $\int_0^\infty{\frac{\tan x}{x^n}dx}$ 14 Finding $\max |A|$ with $a_{ij}=\pm 1$

### Reputation (3,418)

 +26 A twisted hypergeometric series $\sum_{n=1}^\infty\frac{H_n}{n}\left(\frac{(2n)!}{4^n(n!)^2}\right)^2$ +5 Functional equation of $\sum_{n=0}^\infty \chi(n)x^n$ +5 Is $\cot(\cot(\cot(\cdots\cot1)\cdots))$ always defined? +5 Finding $\limsup_{n\to\infty}\sum_{k=0}^n(-1)^k|\sin k|$

 13 Evaluate $\int_0^1 \log \left( \frac{x^2+\sqrt{3}x+1}{x^2-\sqrt{3}x+1} \right) \frac{dx}{x}$ 6 How to prove $\int_0^\infty \ln(1+\frac{z}{\cosh(x)})dx=\frac{\pi^2}{8}+\frac{(\cosh^{-1}(z))^2}{2},z\ge1$ and a closed form for \$-1

### Tags (76)

 38 integration × 47 11 closed-form × 4 37 definite-integrals × 48 10 polylogarithm × 10 36 calculus × 51 9 special-functions × 13 21 improper-integrals × 6 7 complex-analysis × 14 16 sequences-and-series × 15 7 limits × 10

### Accounts (7)

 Mathematics 3,418 rep 1845 Area 51 154 rep 5 Chemistry 148 rep 6 MathOverflow 123 rep 5 Arqade 116 rep 3