Mathematics
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Vivek Kaushik
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Mathematics Ph.D. Student at University of Illinois Urbana Champaign.

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All Questions Answers
Score Newest
answer
19
Prove $\int_{0}^{\infty}\frac{2x}{x^8+2x^4+1}dx=\frac{\pi}{4}$
May 30, 2016
question
18
A Challenging Integral: $\int_{0}^{1} \frac{x \arcsin(x/2) \log(x)}{x^2-1} \ dx=\frac{5 \pi^3}{1296}$
Feb 13, 2019
answer
18
Proving $\left(1-\frac13+\frac15-\frac17+\cdots\right)^2=\frac38\left(\frac1{1^2}+\frac1{2^2}+\frac1{3^2}+\frac1{4^2}+\cdots\right)$
Sep 19, 2019
answer
16
Nice proofs of $\zeta(4) = \frac{\pi^4}{90}$?
May 22, 2016
answer
10
Quadruple Integral $\int\limits_0^1\!\!\int\limits_0^1\!\!\int\limits_0^1\!\!\int\limits_0^1\frac1{1-xyzw}\,dw\,dz\,dy\,dx$
Jun 28, 2017
answer
8
Different methods to compute $\sum\limits_{k=1}^\infty \frac{1}{k^2}$ (Basel problem)
Aug 13, 2015
answer
8
Proving $\int_{0}^{\infty} \mathrm{e}^{-x^2} dx = \frac{\sqrt \pi}{2}$
Aug 13, 2015
answer
8
What is the Jacobian matrix?
May 26, 2016
answer
8
Prove $\lim_{x\to 1} \frac{x+2}{x^2+1}=\frac{3}{2}$
Sep 10, 2017
answer
7
Proof of Fresnel's Integral
Dec 9, 2016

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