I need proof .$\int^{\infty}_{0} e^{-at^2} \cos(2 x t) \, dt = \frac{1}{2} \sqrt{\frac{\pi}{a}} e^{\frac{-x^2}{a}}$.
105494
Gaussian-like integral : $\int_0^{\infty} e^{-x^2} \cos( a x) \ \mathrm{d}x$
27347
Verify that $\left|\int_{\gamma} \exp(iz^2)dz\right| \leq \frac{\pi\big(1-\exp(-r^2)\big)}{4r}$ where $\gamma(t)=re^{it}$, for $0\leq t \leq \pi/4$.
98836
Showing $\int_x^{x+1}f(t)\,dt \xrightarrow{x\to\infty}0$ for $f\in L^2 (\mathbb{R})$
79908
Show $\int_0^\infty \frac{e^{-x}-e^{-xt}}{x}dx = \ln(t),$ for $t \gt 0$
1516
How did you prove this integral?
62450
Computing $ \int_0^{2\pi} \frac{1}{a^2\cos^2 t+b^2 \sin^2 t} dt \;; a,b>0$.
69301
If $\int_{0}^{x}f(t)dt\rightarrow \infty$ as $|x|\rightarrow \infty\;,$ Then every line $y=mx$ Intersect $ y^2+\int_{0}^{x}f(t)dt=2$
63193
Proof that $\vert\int_a^bf(t)dt\vert\le\int_a^b\vert f(t)\vert dt $ for complex integration
136195
Stuck trying to prove that $e^{-x^{-2}}$ is $C^{\infty}$
16775
Showing that $\int_{0}^{\infty} \frac{dx}{1 + x^2} = 2 \int_0^1 \frac{dx}{1 + x^2}$
31716
Calculate :$\int_{0}^{2\pi }e^{R{ {\cos t}}}\cos(R\sin t+3t)\mathrm{d}t$
19514
$\int_0^{\infty } \frac{\log (x)}{e^x+1} \, dx = -\frac{1}{2} \log ^2(2)$ How to show?
69124
Integral $\int_{0}^{\infty}e^{-ax}\cos (bx)\operatorname d\!x$
13747
Proof of $\int_0^\infty \frac{\sin x}{\sqrt{x}}dx=\sqrt{\frac{\pi}{2}}$
41372
Stuck on crucial step while computing $\int_{- \infty}^{\infty} e^{-t^2}dt$
28053
Integral of $\sin(e^t)dt$
11757
How can I compute the integral $\int_{0}^{\infty} \frac{dt}{1+t^4}$?