# xpaul

less info
reputation
1021
bio website location age member for 1 year, 9 months seen 4 hours ago profile views 339

 14 Funny identities 13 Nice proofs of $\zeta(4) = \pi^4/90$? 12 Evaluating $\int_0^{\infty}\frac{\ln(x^2+1)}{x^2+1}dx$ 10 Integrate $\left[\arctan\left(x\right)/x\right]^{2}$ between $-\infty$ and $+\infty$ 9 Closed form for the integral $\int_{0}^{\infty}\frac{\ln^{2}(x)\ln(1+x)}{(1-x)(x^{2}+1)}dx$

# 4,773 Reputation

 +50 Evaluating $\int_0^\infty \frac{\log (1+x)}{1+x^2}dx$ +10 How to compute the integral $\int^{\pi/2}_0\ln(1+\tan\theta)d\theta$? +10 Evaluate $\int_0^{\pi/2}x\cot{(x)}\ln^4\cot\frac{x}{2}\,\mathrm dx$ +10 Integral $\int_0^\infty \log^2 x\frac{1+x^2}{1+x^4}dx=\frac{3 \pi^3}{16\sqrt 2}$

# 5 Questions

 20 Closed form for $\sum_{n=-\infty}^{\infty}\frac{1}{(n-a)^2+b^2}$. 4 Is $AB+BA$ positive definite too if $A$ and $B$ are positive definite? 0 How to show $\lim_{n\to\infty}\frac{(2n+1)!!}{2^nn!(2n-1)}=0$? 0 Prove or disprove a result for a double sequence. [closed] -2 Does $\pi$ contain the combination 1234567890? [closed]

# 82 Tags

 211 calculus × 107 91 complex-analysis × 42 190 integration × 75 63 sequences-and-series × 23 122 definite-integrals × 46 31 contour-integration × 10 112 real-analysis × 56 28 limits × 16 99 improper-integrals × 39 22 analysis × 12

# 2 Accounts

 Mathematics 4,773 rep 1021 Android Enthusiasts 101 rep