# shobhit.iands

less info
reputation
2940
bio website integralsandseries.prophpbb.c… location age member for 1 year, 2 months seen 6 hours ago profile views 705

# 27 Questions

 49 Evaluate $\int_0^1 \frac{\log \left( 1+x^{2+\sqrt{3}}\right)}{1+x}dx$ 22 Prove $\int_0^1 \frac{t^2-1}{(t^2+1)\log t}dt = 2\log\left( \frac{2\Gamma \left( \frac{5}{4}\right)}{\Gamma\left( \frac{3}{4}\right)}\right)$ 16 Evaluating $\int_0^1 \frac{\log x \log \left(1-x^4 \right)}{1+x^2}dx$ 15 Prove $\int_0^\infty \frac{\ln(\tan^2 (ax))}{1+x^2}dx = \pi\ln(\tanh(a))$ 14 Proving a formula for $\int_0^\infty \frac{\log(1+x^{4n})}{1+x^2}dx$ if $n=1,2,3,\cdots$

# 2,794 Reputation

 +10 A closed form for $\int_0^\infty\frac{\ln(x+4)}{\sqrt{x\,(x+3)\,(x+4)}}dx$ +10 Evaluation of the integral $\int_0^1 \log{\Gamma(x+1)}\mathrm dx$ +5 Evaluate $\int_0^1 \frac{\log \left( 1+x^{2+\sqrt{3}}\right)}{1+x}dx$ +10 Evaluating $‎\sum_{n=2}^{\infty}\frac{\zeta(n)}{k^n}$

 34 Closed form for $\int_0^1\sqrt{\frac{2-x}{(1-x)\,x}}\,\log\left(\frac{(2-x)\,x}{1-x}\right)dx$ 23 Integral $\int_0^\infty\frac{1}{x\,\sqrt{2}+\sqrt{2\,x^2+1}}\cdot\frac{\log x}{\sqrt{x^2+1}}\mathrm dx$ 14 Integral $\int_0^1\frac{\log(1-x)}{\sqrt{x-x^3}}dx$ 14 A Tough Series $\sum_{k=1}^\infty \frac{\zeta(2k+1)-1}{k+1}=-\gamma+\log(2)$ 12 Evaluating $‎\sum_{n=2}^{\infty}\frac{\zeta(n)}{k^n}$

# 26 Tags

 102 integration × 22 45 improper-integrals × 12 96 closed-form × 13 29 sequences-and-series × 12 91 calculus × 13 26 riemann-zeta × 4 79 definite-integrals × 18 17 summation × 4 68 logarithms × 4 11 analysis × 10

# 5 Accounts

 Mathematics 2,794 rep 2940 Chemistry 113 rep 4 Physics 101 rep Mathematica 101 rep 1 MathOverflow 101 rep