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Quanto
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37
How deep is the liquid in a half-full hemisphere?
Sep 22, 2019
37
Compute close-form of $\int_0^{\frac\pi2}\frac{dt}{\sin t+\cos t+\tan t+\cot t+\csc t+\sec t}$
Mar 11, 2021
34
Evaluating $\left.\int_0^{\pi/2}\sqrt{1+\frac1{\sqrt{1+\tan^nx}}}\text dx \middle/\int_0^{\pi/2}\sqrt{1-\frac1{\sqrt{1+\tan^nx}}}\text dx\right.$
Dec 8, 2020
31
How to integrate$\int_0^1 \frac{\ln x}{x-1}dx$ without power series expansion
Oct 22, 2019
31
Prove $\cos 20^\circ \cos 40^\circ \cos 80^\circ= \frac18$ geometrically
May 4, 2020
29
Various ways to calculate $\int \sin(x) \cos(x) \, \mathrm{d}x$
Sep 28, 2021
27
When to differentiate under the integral sign?
Nov 27, 2019
26
Solve $\int_0^\infty\frac{\ln(2e^x-1)}{e^x-1}dx$
Feb 17, 2024
24
$\int_{0}^{\infty}\tan^{-1}\left(\frac{2x}{1+x^2}\right)\frac{x}{x^2+4}dx$
Sep 11, 2022
22
Any different way to solve $\int_0^{2\pi}\frac{\sin x+1}{\cos x+2}dx $
Jul 26, 2023