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Vivek Kaushik

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

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19 Prove $\int_{0}^{\infty}\frac{2x}{x^8+2x^4+1}dx=\frac{\pi}{4}$ May 30 '16
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 '19
12 Nice proofs of $\zeta(4) = \frac{\pi^4}{90}$? May 22 '16
10 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 '19
9 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 '17
8 Prove $\lim_{x\to 1} \frac{x+2}{x^2+1}=\frac{3}{2}$ Sep 10 '17
8 Different methods to compute $\sum\limits_{k=1}^\infty \frac{1}{k^2}$ (Basel problem) Aug 13 '15
8 Proving $\int_{0}^{\infty} \mathrm{e}^{-x^2} dx = \frac{\sqrt \pi}{2}$ Aug 13 '15
7 Proof of Fresnel's Integral Dec 9 '16
6 What is the Jacobian matrix? May 26 '16
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