Kemono Chen

Questions (64)

 26 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 (3,548)

 +10 Conjecture $\Re\,\operatorname{Li}_2\left(\frac12+\frac i6\right)=\frac{7\pi^2}{48}-\frac13\arctan^22-\frac16\arctan^23-\frac18\ln^2(\tfrac{18}5)$ +5 An AMM-like integral $\int_0^1\frac{\arctan x}x\ln\frac{(1+x^2)^3}{(1+x)^2}dx$ +5 Evaluating $\int_0^1\ln(1+x^2)\ln(x^2+x^3)\frac{dx}{1+x^2}$ +10 Evaluating $\sum_{n=1}^\infty\frac{(H_n)^2}{n}\frac{\binom{2n}n}{4^n}$

 13 Evaluate $\int_0^1 \log \left( \frac{x^2+\sqrt{3}x+1}{x^2-\sqrt{3}x+1} \right) \frac{dx}{x}$ 9 Evaluating $\sum_{n=1}^\infty\frac{(H_n)^2}{n}\frac{\binom{2n}n}{4^n}$ 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)

 43 definite-integrals × 48 11 closed-form × 4 42 calculus × 51 10 polylogarithm × 10 38 integration × 47 9 special-functions × 13 22 sequences-and-series × 15 9 limits × 11 21 improper-integrals × 6 9 harmonic-numbers × 2

Accounts (7)

 Mathematics 3,548 rep 1847 Chemistry 166 rep 6 Area 51 154 rep 5 MathOverflow 123 rep 5 Arqade 116 rep 3