Integrate x* 2*alpha*x*e^(-alpha*x^2) dx with limits infinity and zero?

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- January 16th 2013, 09:44 AMJDAWESIntegration by parts
Integrate x* 2*alpha*x*e^(-alpha*x^2) dx with limits infinity and zero?

- January 16th 2013, 10:36 PMsbhatnagarRe: Integration by parts
- January 17th 2013, 12:06 PMzaidalyafeyRe: Integration by parts

we can here use the substitution

so we get the following :

Now this is solved by the Laplace transform or gamma function which converges for

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Now for the integrand :

here if we use the same sub we get :