query: How can I solve $\int_{-\infty}^{+\infty}\mathrm{e}^{-(\alpha +\beta i)x^{2}}\mathrm{d}x$?
positive_passages.docid: 100559
positive_passages.text: Gaussian integral with a shift in the complex plane
negative_passages.docid: 66902
negative_passages.text: Prove that $\int_{-\infty}^{\infty} \frac{e^{2x}-e^x}{x (1+e^{2x})(1+e^{x})}\mathrm{d}x=\log 2$
negative_passages.docid: 31063
negative_passages.text: Evaluating $\int_0^2(\tan^{-1}(\pi x)-\tan^{-1} x)\,\mathrm{d}x$
negative_passages.docid: 10319
negative_passages.text: Definite Integral $\int_{-\infty}^{\infty}\frac{x\sin x}{(x^2+a^2)(x^2+b^2)}\,\mathrm{d}x$
negative_passages.docid: 33155
negative_passages.text: Use residues to evaluate $\int_0^\infty \frac{\cosh(ax)}{\cosh(x)}\,\mathrm{d}x$, where $|a|<1$
negative_passages.docid: 70830
negative_passages.text: How to evaluate $\int_{0}^{\infty}\exp(-x^2-1/x^2)dx$?
negative_passages.docid: 144039
negative_passages.text: Computing $ \int_0^{\infty} \frac{ \sqrt [3] {x+1}-\sqrt [3] {x}}{\sqrt{x}} \mathrm dx$
negative_passages.docid: 133485
negative_passages.text: How to solve $\int_0^{\infty} \frac{\log(x+\frac{1}{x})}{1+x^2}dx$?
negative_passages.docid: 14385
negative_passages.text: Solve $\int \limits_{0}^{\infty} \frac{\cos(x)}{\cosh(x)} dx$ without complex integration.
negative_passages.docid: 137549
negative_passages.text: Given $\int_0^{\infty}e^{-x^2}dx = \frac{\sqrt{\pi}}{2}$, evaluate $\int_0^{\infty}e^{-a^2x^2-\frac{b^2}{x^2}}dx $
negative_passages.docid: 96505
negative_passages.text: Compute $\int_0^\infty \left(\frac{1}{x}\right)^{\ln(x)}\,\mathrm{d}x$
negative_passages.docid: 95426
negative_passages.text: How to compute $ \frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty \frac{e^{-{x^2}/{2}}}{1+e^{-(ax+b)}}\,\mathrm dx $ when $b \ne 0$
negative_passages.docid: 29383
negative_passages.text: Computing $\int_{-\infty}^{\infty} \frac{\cos x}{x^{2} + a^{2}}dx$ using residue calculus
negative_passages.docid: 71700
negative_passages.text: How to solve $\int_0^\pi{\frac{\cos{nx}}{5 + 4\cos{x}}}dx$?
negative_passages.docid: 765
negative_passages.text: $\int_0^\infty \frac{\log(x)}{x^2+\alpha^2}$ using residues
negative_passages.docid: 123694
negative_passages.text: How to compute the integral $\int_{0}^{\infty} \frac{x^{1/3}}{1+x^{2}} \ dx$
negative_passages.docid: 119410
negative_passages.text: Solution of $\int_0^\infty\frac{\ln(1+{x^2})}{1+{x^2}}$