sos440
Reputation
39,117
862/400 score
3 83 145
Impact
~243k people reached

 114 A math contest problem $\int_0^1\ln\left(1+\frac{\ln^2x}{4\,\pi^2}\right)\frac{\ln(1-x)}x \ \mathrm dx$ 96 Integral $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \ \mathrm dx$ 96 Prove that $\frac{100!}{50!\cdot2^{50}} \in \Bbb{Z}$ 71 Evaluating $\lim_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$ 53 How to show that $\int_0^1 \left(\sqrt[3]{1-x^7} - \sqrt[7]{1-x^3}\right)\;dx = 0$

### Reputation (39,117)

 +10 Can I get better approximation of $\sum_{k=1}^{n} k^k$ +10 Evaluate the integral $\int_{0}^{\infty} \frac{1}{(1+x^2)\cosh{(ax)}}dx$ +10 Difficult integral? +10 An integral involving Fresnel integrals $\int_0^\infty \left(\left(2\ S(x)-1\right)^2+\left(2\ C(x)-1\right)^2\right)^2 x\ \mathrm dx,$

### Questions (21)

 45 How much does symbolic integration mean to mathematics? 43 Polynomial equations $p(A, B) = 0$ for matrices that ensure $AB = BA$ 40 Extending the result $\int_{0}^{\infty} \left( ( 1 - 2C(x))^{2} + (1-2S(x))^{2} \right) \, dx = \frac{4}{\pi}$ 34 Integral $\int_{-1}^{1} \frac{1}{x}\sqrt{\frac{1+x}{1-x}} \log \left( \frac{(r-1)x^{2} + sx + 1}{(r-1)x^{2} - sx + 1} \right) \, \mathrm dx$ 33 Generalizing $\int_{0}^{1} \frac{\arctan\sqrt{x^{2} + 2}}{\sqrt{x^{2} + 2}} \, \frac{\operatorname dx}{x^{2}+1} = \frac{5\pi^{2}}{96}$

### Tags (161)

 2k calculus × 128 467 improper-integrals × 38 1k integration × 131 452 closed-form × 24 862 definite-integrals × 69 357 limits × 53 608 real-analysis × 89 187 trigonometry × 16 517 sequences-and-series × 88 182 special-functions × 18

### Accounts (4)

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