query: How do I evaluate the following integral $\int_{-\infty}^{\infty} e^{-\sigma^2 x^2/2}\; \mathrm dx$?
positive_passages.docid: 4287
positive_passages.text: Proving $\int_{0}^{\infty} \mathrm{e}^{-x^2} dx = \frac{\sqrt \pi}{2}$
negative_passages.docid: 60654
negative_passages.text: Integrate $\int_0^{2 \pi } \frac{1}{(a+b \cos^2 (x))^2} \, \mathrm{d}x$
negative_passages.docid: 93071
negative_passages.text: Is there a way to calculate the improper integral $\int_0^\infty \big(\frac{\ln x}{x - 1}\big)^2 dx$?
negative_passages.docid: 107351
negative_passages.text: Evaluate the improper integral $\int_{0}^{\infty}{f(x)-f(2x)\over x}dx$, where $\lim_{x \to \infty} f(x) = L$
negative_passages.docid: 15569
negative_passages.text: Integral of the form $\int_0^\infty \exp{\left(-\frac{(a+bx)^2}{x}\right)}\frac{dx}{\sqrt{x^3}}$
negative_passages.docid: 65407
negative_passages.text: Evaluating $\int\limits_0^\infty \frac{\log x} {(1+x^2)^2} dx$ with residue theory
negative_passages.docid: 111775
negative_passages.text: $\int_{-\infty}^{+\infty} e^{-x^2} dx$ with complex analysis
negative_passages.docid: 70830
negative_passages.text: How to evaluate $\int_{0}^{\infty}\exp(-x^2-1/x^2)dx$?
negative_passages.docid: 87273
negative_passages.text: Evaluate the integral $\int_0^{\infty} \lfloor x \rfloor e^{-x}\mathrm dx$
negative_passages.docid: 150890
negative_passages.text: Evaluating $\int_{\mathbb{R}}\frac{\exp(-x^2)}{1+x^2}\,\mathrm{d}x$
negative_passages.docid: 100569
negative_passages.text: Evaluating the improper integral $\int_{0}^{\infty} \frac{x^3}{e^{x}-1} dx$
negative_passages.docid: 69978
negative_passages.text: Evaluating $\int_1^\infty \frac{1}{x(x^2+1)}\ dx$
negative_passages.docid: 117602
negative_passages.text: How to evaluate $\int \cot^2(x) \;\mathrm dx$?
negative_passages.docid: 34855
negative_passages.text: Evaluate the integral: $\int_{0}^{1} \frac{\ln(x+1)}{x^2+1} \mathrm dx$
negative_passages.docid: 67322
negative_passages.text: evaluate $\int_{0}^{\infty}\cos(t) t^{z-1}dt=\Gamma(z)\cos(\frac{\pi z}{2})$
negative_passages.docid: 96191
negative_passages.text: Integral $\int_0^{\infty} \sin(x^2)/x^2\,dx$
negative_passages.docid: 89956
negative_passages.text: Is the integral $\int_0^\infty \frac{\mathrm{d} x}{(1+x^2)(1+x^a)}$ equal for all $a \neq 0$?