Mathematics
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NoName
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View all questions and answers
All Questions Answers
Score Newest
answer
22
Interesting Integral including $\ln x$
Apr 20, 2021
answer
20
Feynman's trick to evaluate the integral $\int\limits_{0}^{2\pi}\sin^{8}(x)dx$
May 20, 2021
answer
20
Showing $\int_{0}^{2\pi}\cos(x)\cos(2x)\cos(3x)\,dx = \frac\pi2$
Jul 5, 2021
answer
10
How to prove $\int_0^1\frac{1-x}{(\ln x)(1+x)}\ dx=\ln\left(\frac2{\pi}\right)$?
Aug 30, 2019
answer
10
Show that $\sum_{n=0}^\infty \frac{1}{n+1} \binom{2n}{n} \frac{1}{2^{2n+1}} = 1.$
Feb 13, 2020
answer
9
Closed form of the sum $\sum _{n=1}^{\infty }\:\left(\frac{1}{x^2-n^2\pi ^2}\right)$
Apr 8, 2021
answer
7
Evaluate $\int_0^\infty \frac{e^{-x}}{x}\ln\big(\frac{1}{x}\big) \sin(x)dx$
Sep 9, 2021
answer
6
Closed-form expression for $F(x,y) = \int_0^1 \frac{\sqrt{t(1-t)}}{(t+x)^2 (t+y)} \mathrm{d}t$?
Feb 15, 2020
answer
6
Having the sequence $(a_{n})_{n\geq1}$, $a_{n}=\int_{0}^{1} x^{n}(1-x)^{n}dx$, find $\lim\limits_{n{\rightarrow}\infty} \frac{a_{n+1}}{a_{n}}$
Mar 3, 2019
answer
5
Infinite product of $\sqrt{2}$
Nov 9, 2020

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