Integrate x^(5/2) e^(-x): Solving w/ Substitution & √2π

[nikhilb1997]

Homework Statement

Using \int_{-\infty}^{\infty}e^{-x^2/2} dx = \sqrt{2\pi}, Integrate x^(5/2) e^(-x) dx from 0 to infinty

2. The attempt at a solution
I tried substituting x = u^2/2 but i could not simplify further.
Please help me with the problem.
Thank you in advance.

 

[Orodruin]

You are supposed to use the knowledge of the result of the given integral to find out the integral you want. Changing the integral to one with $-x$ in the exponent instead of $-x^2/2$ is a good start. I also suggest looking up Feynman's trick of differentiating an integral with respect to a parameter (not the integration variable) and changing the order of integration and differentiation.

 

[nikhilb1997]

You are supposed to use the knowledge of the result of the given integral to find out the integral you want. Changing the integral to one with $-x$ in the exponent instead of $-x^2/2$ is a good start. I also suggest looking up Feynman's trick of differentiating an integral with respect to a parameter (not the integration variable) and changing the order of integration and differentiation.

Thanks a lot feynman's trick was a good read. But if suppose i did have to use the given result then, what would be the method to go forward with?

 

[Orodruin]

I would use Feynman's trick together with the given result. The alternative is doing partial integration. It all is going to boil down to evaluation of the given integral in the end.

 

[nikhilb1997]

I would use Feynman's trick together with the given result. The alternative is doing partial integration. It all is going to boil down to evaluation of the given integral in the end.

I was just trying it i understood how it works. I should be able to use both together. Thanks a lot.