Chris's sis the artist
Reputation
18,745
Top tag
Next privilege 20,000 Rep.
Access 'trusted user' tools
4 42 176
Impact
~260k people reached

### Questions (295)

 85 Evaluating $\lim_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$ 77 Prove elementarily that $\sqrt[n+1] {(n+1)!} - \sqrt[n] {n!}$ is strictly decreasing 47 Evaluate the integral: $\int_{0}^{1} \frac{\ln(x+1)}{x^2+1} \mathrm dx$ 42 Prove that $\int_0^{\infty} \frac{\sin(2013 x)}{x(\cos x+\cosh x)}dx=\frac{\pi}{4}$ 41 Evaluate $\int_0^1\left(\frac{1}{\ln x} + \frac{1}{1-x}\right)^2 \mathrm dx$

### Reputation (18,745)

 +36 Another beautiful arctan integral $\int_{1/2}^1 \frac{\arctan\left(\frac{1-x^2}{7 x^2+10x+7}\right)}{1-x^2} \, dx$ +40 Another beautiful integral (Part 2) +10 A tricky sum to infinity +5 Calculating in closed form $\sum_{n=1}^{\infty} \sum_{m=1}^{\infty} \frac{1}{m^4(m^2+n^2)}$

 51 The last digit of $2^{2006}$ 26 Evaluating $\int_0^{\frac\pi2}\frac{\ln{(\sin x)}\ \ln{(\cos x})}{\tan x}\ dx$ 22 Prove $\int_0^1 \frac{t^2-1}{(t^2+1)\log t}dt = 2\log\left( \frac{2\Gamma \left( \frac{5}{4}\right)}{\Gamma\left( \frac{3}{4}\right)}\right)$ 19 Evaluate $\int_0^{\pi/2}\frac{x^2\log^2{(\sin{x})}}{\sin^2x}dx$ 19 How to integrate $\int_1^e \ln{x} \, dx$

### Tags (81)

 384 calculus × 329 149 improper-integrals × 42 321 integration × 178 138 real-analysis × 299 213 definite-integrals × 119 59 inequality × 47 206 limits × 167 57 closed-form × 12 166 sequences-and-series × 158 52 trigonometry × 25

### Accounts (9)

 Mathematics 18,745 rep 442176 Mathematica 689 rep 215 English Language & Usage 121 rep 27 Meta Stack Exchange 101 rep 1 TeX - LaTeX 101 rep 1