$\int_{-\infty}^{\infty} e^{-\xi^2t}e^{i\xi x}d\xi$
23059
How to calculate the Fourier transform of a Gaussian function?
152339
Complex-valued Fourier integral: $ \int_{ - \infty }^{ + \infty } {\frac{{\cos (ax)}}{{{x^2} + 1}}{e^{ - ibx}}\,\mathrm dx} $
40564
Prove that $u(x,t)=\int_{-\infty}^{\infty}c(w)e^{-iwx}e^{-kw^2t}dw\rightarrow 0$ if $x\rightarrow \infty$
15625
Computing $\int_0^\infty\mathrm{d} x\frac{x}{e^x+1}$ with contour integration
21375
The integral $\int_0^\infty \dfrac{x \sin(x)}{x^2+1} dx$
79908
Show $\int_0^\infty \frac{e^{-x}-e^{-xt}}{x}dx = \ln(t),$ for $t \gt 0$
61133
Show that $\int|f(x)|dx=\int_0^\infty m(E_\alpha)d\alpha$
94395
Integral: $\int_{-\infty}^{\infty} x^2 e^{-x^2}\mathrm dx$
100711
$\int_{-\infty}^{\infty}e^{-zt^2 + 2wt} \ dt = e^{w^2 / z} \sqrt{\frac{\pi}{z}}$ for $z,w \in \mathbb{C}, Re(z) > 0$
41372
Stuck on crucial step while computing $\int_{- \infty}^{\infty} e^{-t^2}dt$
97039
Use integral test to show that Gaussian Integral $\int_{-\infty}^{\infty} e^{-x^2} \ dx$ converges?
142516
Evaluating the integral, $\int_{0}^{\infty} \ln\left(1 - e^{-x}\right) \,\mathrm dx $
69978
Evaluating $\int_1^\infty \frac{1}{x(x^2+1)}\ dx$
128572
How $\int_{-\infty}^{\infty}\frac{dx}{1+x^2}$ exists?
13747
Proof of $\int_0^\infty \frac{\sin x}{\sqrt{x}}dx=\sqrt{\frac{\pi}{2}}$
66902
Prove that $\int_{-\infty}^{\infty} \frac{e^{2x}-e^x}{x (1+e^{2x})(1+e^{x})}\mathrm{d}x=\log 2$
102636
Contour Integral: $\int^{\infty}_{0}(1+z^n)^{-1}dz$