# Linked Questions

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I would like to compute an integral of the form ($a,b \neq 0$) $$\int_{-\infty}^{\infty} e^{-(ax+ib)^2} dx = \frac{1}{a} \int_{-\infty+ib}^{\infty+ib} e^{-z^2} dz$$ where we made the substitution $z ... 2answers 106 views ### Strange integrand Is it possible, and if yes, how, to evaluate an integral like$\int \sqrt{x} e^{x}dx$? I have hear of the Gaussian function which integrates to$\sqrt{\pi}$but what about this? Thank you. 3answers 2k views ###$\int e^{-x^2}dx$[duplicate] Possible Duplicate: Proving$\int_{0}^{\infty} e^{-x^2} dx = \frac{\sqrt \pi}{2}$How does one integrate$\int e^{-x^2}\,dx$? I read somewhere to use polar coordinates. How is this done? What ... 1answer 595 views ### Computing the integral of$e^{-x^2}$over the entire line [duplicate] Possible Duplicate: Proving$\\int_{0}^{+\\infty} e^{-x^2} dx = \\frac{\\sqrt \\pi}{2}\$ At lunch with a math friend years ago, he showed me an integral whose solution was, he said, so beautiful ...

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