query: How would I go about evaluating $\int_{0}^{\infty}e^{{-u}^{2}}\cos(ux)du$?
positive_passages.docid: 105494
positive_passages.text: Gaussian-like integral : $\int_0^{\infty} e^{-x^2} \cos( a x) \ \mathrm{d}x$
negative_passages.docid: 128600
negative_passages.text: How to evaluate this integral$\int_{-\infty}^\infty\dfrac{\omega^\alpha e^{i\omega t}}{(\omega_0^2-\omega^2)^{2}+4(\zeta\omega_0\omega)^2}\,d\omega$
negative_passages.docid: 89602
negative_passages.text: $ \int_{0}^{ \infty} \int_{0}^{ \infty} \frac { e^{-(x+y)}}{x+y} dx dy $
negative_passages.docid: 84034
negative_passages.text: Evaluate $\int_{-\infty}^{\infty} \chi_{[0,1]}(x-y) \chi_{[0,1]}(y) \, \mathrm{d}y$
negative_passages.docid: 19475
negative_passages.text: Evaluate$\int_{-2}^2\int_{y^2-3}^{5-y^2}dxdy$
negative_passages.docid: 81258
negative_passages.text: Evaluation of $\int_{-\infty}^\infty \frac{\sin(at)}t\ dt$
negative_passages.docid: 85081
negative_passages.text: $\int_{0}^{\infty} \frac{\cos x - e^{-x}}{x} \mathrm dx$ Evaluate Integral
negative_passages.docid: 124463
negative_passages.text: Integral from $0$ to $\infty$ of $\ln(x)/e^x$
negative_passages.docid: 130058
negative_passages.text: Evaluate $\int_0^{\pi} e^{a\cos(t)}\cos(a\sin t)dt$
negative_passages.docid: 81621
negative_passages.text: How to evaluate the integral $\int_{0}^{\infty}\frac{\cos {(ax)}-\cos{(b x)}}{x^2 }dx$?
negative_passages.docid: 41372
negative_passages.text: Stuck on crucial step while computing $\int_{- \infty}^{\infty} e^{-t^2}dt$
negative_passages.docid: 156531
negative_passages.text: Evaluating the integral $\int_{-\infty}^\infty \frac{\sin^2(x)}{x^2}e^{i t x} dx$
negative_passages.docid: 114195
negative_passages.text: Evaluating $\int_0^\infty \frac{\log (1+x)}{1+x^2}dx$
negative_passages.docid: 24022
negative_passages.text: Compute $\int _0 ^{2\pi} (\sum_{n=1}^\infty \frac {\cos(nx)}{2^n})^2 dx$
negative_passages.docid: 100569
negative_passages.text: Evaluating the improper integral $\int_{0}^{\infty} \frac{x^3}{e^{x}-1} dx$
negative_passages.docid: 121071
negative_passages.text: Calculation of $\int^{\pi/2}_{0}\cos^{n}(x)\cos (nx)\,dx$, where $n\in \mathbb{N}$
negative_passages.docid: 54735
negative_passages.text: What is the closed form of $\int e^{x^2} \, dx$?