query: Compute the integral $\int_{0}^{\infty} \exp(in\omega t-\gamma^2 t^2)dt$
positive_passages.docid: 24558
positive_passages.text: Show that $\frac{1}{\sqrt{2\pi}} \cdot \left(\int_{- \infty}^{\infty} e^{itx} \cdot e^{-\frac{1}{2}t^2 } dx \right) = e^{-\frac{1}{2}t^2}$
negative_passages.docid: 23522
negative_passages.text: Exponential integral $ \int_0^\infty \frac{x^t}{\Gamma(t+1)}\text dt$
negative_passages.docid: 105494
negative_passages.text: Gaussian-like integral : $\int_0^{\infty} e^{-x^2} \cos( a x) \ \mathrm{d}x$
negative_passages.docid: 130058
negative_passages.text: Evaluate $\int_0^{\pi} e^{a\cos(t)}\cos(a\sin t)dt$
negative_passages.docid: 114195
negative_passages.text: Evaluating $\int_0^\infty \frac{\log (1+x)}{1+x^2}dx$
negative_passages.docid: 68319
negative_passages.text: How can I evaluate $\int_{-\infty}^{\infty} e^{-x^2} dx$ without using polar coordinates
negative_passages.docid: 44054
negative_passages.text: Evaluating the integral $\mathop{\lim}\limits_{n \to \infty} \int_{-1}^{1} f(t)\cos^{2}(nt) \ dt $
negative_passages.docid: 31716
negative_passages.text: Calculate :$\int_{0}^{2\pi }e^{R{ {\cos t}}}\cos(R\sin t+3t)\mathrm{d}t$
negative_passages.docid: 81057
negative_passages.text: Evaluation of $\int_{\frac{1}{e}}^{\tan x}\frac{t}{1+t^2}dt+\int_{\frac{1}{e}}^{\cot x}\frac{1}{t(1+t^2)}dt$
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: 68097
negative_passages.text: Prove $\int\limits_{0}^{\infty} \mathrm{exp}(-ax^{2}-\frac{b}{x^{2}}) \mathrm{d} x = \frac{1}{2}\sqrt{\frac{\pi}{a}}\mathrm{e}^{-2\sqrt{ab}}$
negative_passages.docid: 86857
negative_passages.text: Integrate $\int_{0}^{2\pi}\log|1-e^{i\theta}| d\theta$
negative_passages.docid: 113094
negative_passages.text: What is the integral of the gamma function
negative_passages.docid: 98710
negative_passages.text: Finding $\int_0^{\infty}xe^{-\lambda x} \, dx$
negative_passages.docid: 84413
negative_passages.text: Why is $\int_{-\infty}^\infty |g(x)|\,dx = \int_0^\infty \mu(\{x : |g(x)| \ge t\})\,dt$ true?
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: 151127
negative_passages.text: Confirm that $\int_{0}^{\infty}t^{-1}\sin t dt=\pi/2$