Sangchul Lee
Reputation
51,210
1789/1000 score
6 103 177
Impact
~393k people reached

 146 A math contest problem $\int_0^1\ln\left(1+\frac{\ln^2x}{4\,\pi^2}\right)\frac{\ln(1-x)}x \ \mathrm dx$ 121 Integral $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \ \mathrm dx$ 102 Prove that $\frac{100!}{50!\cdot2^{50}} \in \Bbb{Z}$ 90 Evaluating $\lim\limits_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$ 55 How to show that $\int_0^1 \left(\sqrt[3]{1-x^7} - \sqrt[7]{1-x^3}\right)\;dx = 0$

### Reputation (51,210)

 +10 Integral $\int_0^\infty\text{Li}_2\left(e^{-\pi x}\right)\arctan x\,dx$ +10 All real numbers in $[0,2]$ can be represented as $\sqrt{2 \pm \sqrt{2 \pm \sqrt{2 \pm \dots}}}$ +20 Evaluating $\lim\limits_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$ +10 Calculate sums of inverses of binomial coefficients

### Questions (28)

 106 Generalizing $\int_{0}^{1} \frac{\arctan\sqrt{x^{2} + 2}}{\sqrt{x^{2} + 2}} \, \frac{\operatorname dx}{x^{2}+1} = \frac{5\pi^{2}}{96}$ 53 How much does symbolic integration mean to mathematics? 47 Polynomial equations $p(A, B) = 0$ for matrices that ensure $AB = BA$ 43 Extending the result $\int_{0}^{\infty} \left( ( 1 - 2C(x))^{2} + (1-2S(x))^{2} \right) \, dx = \frac{4}{\pi}$ 42 Integral $\int_{-1}^{1} \frac{1}{x}\sqrt{\frac{1+x}{1-x}} \log \left( \frac{(r-1)x^{2} + sx + 1}{(r-1)x^{2} - sx + 1} \right) \, \mathrm dx$

### Tags (214)

 2k calculus × 166 593 closed-form × 34 2k integration × 170 534 improper-integrals × 42 1k definite-integrals × 93 430 limits × 68 786 real-analysis × 126 227 trigonometry × 21 670 sequences-and-series × 112 222 contest-math × 9

### Accounts (7)

 Mathematics 51,210 rep 6103177 MathOverflow 216 rep 15 English Language & Usage 163 rep 5 TeX - LaTeX 123 rep 4 Stack Overflow 101 rep 2