sos440

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22658
bio website sos440.tistory.com
location Seoul, South Korea
age 25
visits member for 2 years, 1 month
seen 11 mins ago
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I love mathematics, and especially, calculating some sort of integrals and summations with inner aesthetic appealing.

Language fluency:

  • Korean: Native
  • English: (Reading: Green / Listening : Amber / Speaking : Red / Writing : Amber)
  • Japanese: (Reading : Amber / Listening : Amber / Speaking : Amber / Writing : Red)

249 Answers

newest activity votes
35
How to show that $\int_0^1 \left(\sqrt[3]{1-x^7} - \sqrt[7]{1-x^3}\right)\;dx = 0$
32
Compute $ I_{n}=\int_{-\infty}^\infty \frac{1-\cos x \cos 2x \cdots \cos nx}{x^2}\,dx$
26
$\lim_{n\rightarrow\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$
20
Prove $\int_0^\infty \frac{\ln(\tan^2 (ax))}{1+x^2}dx = \pi\ln(\tanh(a))$
19
Is there a third dimension of numbers?
19
Integrating $\frac{x^k }{1+\cosh(x)}$
17
Compute the series : $\sum_{n=1}^{\infty} \frac{4^n n!}{(2n)!}$
16
Find an expression for the $n$-th derivative of $f(x)=e^{x^2}$
15
$\int_0^{\infty}\frac{x^3}{(x^4+1)(e^x-1)}\mathrm dx$
15
Infinite powering by $ i$
15
Two curious “identities” on $x^x$,$e$,and $\pi$
15
Show $\int_{0}^{\frac{\pi}{2}}\frac{x^{2}}{x^{2}+\ln^{2}(2\cos(x))}dx=\frac{\pi}{8}\left(1-\gamma+\ln(2\pi)\right)$
15
Evaluating $\int_0^1 \log \log \left(\frac{1}{x}\right) \frac{dx}{1+x^2}$
15
Difficult integral?
14
Is $\tan(\pi/2)$ undefined or infinity?
14
Evaluate $\int\limits_0^{\frac{\pi}{2}} \frac{\sin(2nx)\sin(x)}{\cos(x)}\, dx$
14
Closed form of integral.
13
Evaluate $\int_0^1\left(\frac{1}{\ln x} + \frac{1}{1-x}\right)^2 \mathrm{dx}$
13
How to find the Laplace transform of $\frac{1-\cos(t)}{t^2}$?
13
How to evaluate $\lim\limits_{n\to+\infty} \prod\limits_{k=1}^n (1+k/n^2)$?
13
How to evaluate these integrals by hand
13
Another Evaluating Limit Question
12
The function $f(x) = \int_0^\infty \frac{x^t}{\Gamma(t+1)} \, dt$
11
Showing that $\frac{\sqrt[n]{n!}}{n}$ $\rightarrow \frac{1}{e}$
11
How to find the integral $\int_{-\infty}^{\infty}\frac{dx}{1+ae^{bx^2}}$
10
$\int_X |f_n - f| \,dm \leq \frac{1}{n^2}$ for all $n \geq 1$ $\implies$ $f_n \rightarrow f$ a.e.
10
Prove the divergence of the sequence $(\sin(n))_{n=1}^\infty$.
10
A curve whose image has positive measure
10
Evaluating $\int_{0}^{\infty}\frac{\arctan \sin^2x}{x}dx$
10
Difficult integral
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