# sos440

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bio website sos440.tistory.com location Los Angeles, CA age 27 member for 3 years, 8 months seen 2 hours ago profile views 6,866

I am currently a UCLA student, particularly interested in probability theory.

I love mathematics, especially calculating some sort of integrals and summations with inner aesthetic appealing.

Language fluency: (G:green, A:amber, R:red)

• Korean: Native
• English: (Reading: G, Listening : A, Speaking : R, Writing : A)
• Japanese: (Reading : A, Listening : A, Speaking : A, Writing : R)

 108 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 Prove that $\frac{100!}{50!\cdot2^{50}} \in \Bbb{Z}$ 85 Integral $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \ \mathrm dx$ 67 Evaluating $\lim_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$ 53 How to show that $\int_0^1 \left(\sqrt[3]{1-x^7} - \sqrt[7]{1-x^3}\right)\;dx = 0$

# 35,880 Reputation

 +10 Evaluating $\int_0^{\infty }{ \frac{(x^7)(1-x^{12})}{(1+x)^{28}}}dx$ +10 Evaluating $\int_{0}^{\frac{\pi}{2}} \arctan( a \sin x) \ dx$ using the Taylor expansion of $\arctan (x)$ +10 $\int_0^{\infty}\frac{x^3}{(x^4+1)(e^x-1)}\mathrm dx$ +10 Divergent Sequence for Wau

# 19 Questions

 42 How much does symbolic integration mean to mathematics? 41 Polynomial equations $p(A, B) = 0$ for matrices that ensure $AB = BA$ 40 Extending the result $\int_{0}^{\infty} \left( ( 1 - 2C(x))^{2} + (1-2S(x))^{2} \right) \, dx = \frac{4}{\pi}$ 33 Integral $\int_{-1}^{1} \frac{1}{x}\sqrt{\frac{1+x}{1-x}} \log \left( \frac{(r-1)x^{2} + sx + 1}{(r-1)x^{2} - sx + 1} \right) \, \mathrm dx$ 32 Generalizing $\int_{0}^{1} \frac{\arctan\sqrt{x^{2} + 2}}{\sqrt{x^{2} + 2}} \, \frac{\operatorname dx}{x^{2}+1} = \frac{5\pi^{2}}{96}$

# 148 Tags

 1k calculus × 119 446 improper-integrals × 36 1k integration × 124 425 closed-form × 21 776 definite-integrals × 62 339 limits × 48 561 real-analysis × 81 183 trigonometry × 16 465 sequences-and-series × 79 178 special-functions × 18

# 3 Accounts

 Mathematics 35,880 rep 378137 TeX - LaTeX 123 rep 4 MathOverflow 101 rep 2