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Mathematics
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Z Ahmed's user avatar
Z Ahmed
  • Member for 6 years, 11 months
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  • India
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23
Integral $\int_{-\infty}^{\infty} \arctan(e^x) \arctan(e^{-x})dx=\frac{7}{4}\zeta(3)$
Jun 17, 2019
20
Evaluate $\int_{0}^{\infty} \frac{\sin x-x\cos x}{x^2+\sin^2x } dx$
Jul 21, 2019
18
Proving that $\sum_{k=0}^{n}\frac{(-1)^k}{{n\choose k}}=[1+(-1)^n] \frac{n+1}{n+2}.$
Jun 5, 2019
16
Integrate $\int_{0}^{\pi} \frac{1}{1+3^{\cos x}} dx.$
Feb 5, 2020
15
A simple proof for Glasser: $\int_{-\infty}^{\infty} f(x-a/x) dx=\int_{-\infty}^{\infty} f(x) dx, a>0$
Dec 13, 2020
15
Evaluating $\int_{\pi/2}^{\pi} \frac{(\cos x - \sin x) ~dx}{\sin x + \cos x + \sec x + \csc x + \tan x + \cot x} $
Feb 25
14
Proving $\sin(\tanh x) \ge \tanh(\sin x)$, for $x \in [0,\pi/2]$
Mar 30, 2020
11
Evaluate $\iiint_{[0,1]^3}\frac{dx\,dy\,dz}{(1+x^2+y^2+z^2)^2}$
Jul 25, 2019
11
Proving $\int_{0}^{1} \frac{\tanh^{-1}\sqrt{x(1-x)}}{\sqrt{x(1-x)}}dx=\frac{1}{3}(8C-\pi\ln(2+\sqrt{3}))$ for an identity of Srinivasa Ramanujan
Aug 23, 2020
10
Evaluating $\sum_{n=k}^{\infty} \frac{1}{ \binom{n}{k}}$
Sep 17, 2020