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Diffusion
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14
Evaluate $\int_0^{\infty}\frac{\log x}{1+e^x}\,dx$
Dec 30, 2017
14
Evaluation of a Fresnel type integral.
Jun 15, 2018
12
Evaluating the integral $\int_0^{\infty} \frac{\sin(x)}{\sinh(x)}\,dx$
Nov 30, 2017
12
Some horrid integrals I am confused with
Jan 7, 2021
10
Prove that $\int_0^\infty\,\frac{\sin(kx)}{x(x^2+1)}\,\text{d}x=\frac{\pi}{2}\,\left(1-\exp(-k)\right)$ for all $k\in\mathbb{R}_{\ge0}$.
Aug 3, 2018
8
Motion of a falling object with air resistance
Dec 10, 2017
8
How to justify interchange of summation and integral with $f_n(x)=x^2 \cos(2nx)/n$ on $[0, \pi/2]\times \mathbb{N}$?
Aug 21, 2021
7
Why doesn't $\sinh(x)$'s Taylor Series divide by half?
Apr 18, 2018
7
$\int_0^\infty \frac{\sqrt{x}}{x^2+2x+5}\mathrm{d}x$ using Feynman's trick
Jan 17, 2020
7
How should I translate "isomorphisme près" to English?
Mar 29, 2018
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12
Asymptotics of $\int_0^\infty \frac{x^{2z}}{\Gamma(1+z)}\,dz$ for large $x$
12
If $f(x) = \sum_{n=0}^\infty a_n x^n$, then $\int_{-\infty}^\infty f(x^2) dx = \pi i a_{-\frac{1}{2}}$
11
An identity for the elliptic theta function
8
Is there a real-analytic way to derive the asymptotics of $\int_{-\infty}^\infty e^{ikx} e^{-k^4}\,dk$ as $|x|\to\infty$?
7
Bounding the $n$-th derivatives of $\frac{1-\cos(x)}{x^2}$