Show that the standard integral: $\int_{0}^{\infty} x^4\mathrm{e}^{-\alpha x^2}\mathrm dx =\frac{3}{8}{\left(\frac{\pi}{\alpha^5}\right)}^\frac{1}{2}$
44737
$ \int_{-\infty}^{\infty} x^4 e^{-ax^2} dx$
140203
Find the value of $\int_{-\infty}^{\infty} \frac{e^{-x^2}}{1+x^2} dx$ .
123694
How to compute the integral $\int_{0}^{\infty} \frac{x^{1/3}}{1+x^{2}} \ dx$
140638
Integrating $\int_0^{\infty} \frac{dx}{1+x^3}$ using residues.
146349
$\int_0^\infty \frac{\ln\left(1+x-\sqrt{2x}\right)}{1+x^2}\,dx$
46310
Showing that $ \int_{0}^{1} \frac{x-1}{\ln(x)} \mathrm dx=\ln2 $
68821
Prove $\int_0^{\infty} \left(\sqrt{1+x^{4}}-x^{2}\right)\ dx=\frac{\Gamma^{2}\left(\frac{1}{4}\right)}{6\sqrt{\pi}}$
142516
Evaluating the integral, $\int_{0}^{\infty} \ln\left(1 - e^{-x}\right) \,\mathrm dx $
156531
Evaluating the integral $\int_{-\infty}^\infty \frac{\sin^2(x)}{x^2}e^{i t x} dx$
45622
Value of this definite integral $\int_{0}^{\infty} \frac{ \ln(x)}{x^2+2x+4} dx $
105707
A proof of $\int_{0}^{1}\left( \frac{\ln t}{1-t}\right)^2\,\mathrm{d}t=\frac{\pi^2}{3}$
63167
Evaluate integral $\int_0^\frac{\pi}{2} \ln\left(\frac{1+a\cos x}{1-a\cos x}\right) \frac{\mathrm{d} x}{\cos x}$ for $\left|a\right|<1$
36366
Prove $\int_0^\infty \frac{\sin^4x}{x^4}dx = \frac{\pi}{3}$
45205
Showing that $\int_0^\infty x^{-x} \mathrm{d}x \leq 2$.
21390
How to integrate $\int_0^{\infty} \frac{e^{ax} - e^{bx}}{(1 + e^{ax})(1+ e^{bx})}dx$ where $a,b > 0$.
144039
Computing $ \int_0^{\infty} \frac{ \sqrt [3] {x+1}-\sqrt [3] {x}}{\sqrt{x}} \mathrm dx$
136385
Integrate $ \int_{0}^{\frac{\pi}{4}}\tan^{-1}\left(\frac{\sqrt{2}\cos3 \phi}{\left(2\cos 2 \phi+ 3\right)\sqrt{\cos 2 \phi}}\right)d\phi$