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This trick can also be used with the Gaussian integral to compute similar integrals of a Gaussian multiplied with a power of the integration variable [1], e.g.
by fooofw 6y ago
This trick can also be used with the Gaussian integral to compute similar integrals of a Gaussian multiplied with a power of the integration variable [1], e.g. the integral of x*exp(-x^2).
[1] https://en.wikipedia.org/wiki/Gaussian_integral#Integrals_of_similar_form https://en.wikipedia.org/wiki/Gaussian_integral#Integrals_of...
- hpcjoe 6y agoYeah, I used this example in classes I taught. Very awesome application of this technique.
- mjcohen 6y agoOf course the indefinite integral of x*exp(-x^2) is elementary.
- xdavidliu 6y agoI think parent meant to say _even_ powers like x^(2n) exp(-x^2), which can be done by differentiating exp(-Bx^2) and evaluating at B = 1.