I'm an artist
Reputation
19,452
Top tag
Next privilege 20,000 Rep.
Access 'trusted user' tools
4 45 181
Impact
~295k people reached

### Questions (296)

 95 Evaluating $\lim_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$ 79 Prove elementarily that $\sqrt[n+1] {(n+1)!} - \sqrt[n] {n!}$ is strictly decreasing 52 Evaluate the integral: $\int_{0}^{1} \frac{\ln(x+1)}{x^2+1} \mathrm dx$ 43 Evaluate $\int_0^1\left(\frac{1}{\ln x} + \frac{1}{1-x}\right)^2 \mathrm dx$ 43 Prove that $\int_0^{\infty} \frac{\sin(2013 x)}{x(\cos x+\cosh x)}dx=\frac{\pi}{4}$

### Reputation (19,452)

 +11 Another way of doing integration +5 About the integral $\int_{-1}^1 \frac{1}{\pi^2+(2 \operatorname{arctanh}(x))^2} \, dx=\frac{1}{6}$ +5 Evaluation of $\int_0^1 \frac{\log(1+x)}{1+x}\log\left(\log\left(\frac{1}{x}\right)\right) \ dx$ +5 Methods to find $\lim\limits_{n\to\infty} \frac{1}{n} \sum_{k=1}^{n} n^{1/k}$

 53 The last digit of $2^{2006}$ 26 Evaluating $\int_0^{\frac\pi2}\frac{\ln{(\sin x)}\ \ln{(\cos x})}{\tan x}\ dx$ 24 How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$? 22 Prove $\int_0^1 \frac{t^2-1}{(t^2+1)\log t}dt = 2\log\left( \frac{2\Gamma \left( \frac{5}{4}\right)}{\Gamma\left( \frac{3}{4}\right)}\right)$ 20 Evaluate $\int_0^{\pi/2}\frac{x^2\log^2{(\sin{x})}}{\sin^2x}dx$

### Tags (84)

 417 calculus × 333 152 improper-integrals × 43 325 integration × 180 147 real-analysis × 300 226 definite-integrals × 122 69 trigonometry × 29 222 limits × 168 69 closed-form × 12 173 sequences-and-series × 158 62 inequality × 47

### Accounts (9)

 Mathematics 19,452 rep 445181 Mathematica 709 rep 315 English Language & Usage 121 rep 27 MathOverflow 112 rep 7 Meta Stack Exchange 101 rep 1