Doing the integral of a* (x^2) * e^-bx

Question

Hi, I’m having trouble at doing the integral of a*x^2 * e^-bx

. In fact I don’t know how to change the e^-bx to have an answer which , with the definite integral from zero to + infinite, give me a function ( i need to isolate the a after I did the Integral)

Thank you in advance !!!!

Answer 1

You use integration by parts twice. You can easily generalize to the integral of xⁿ e^-bx on [0, ∞)

The integral is n! / bⁿ⁺¹

Thus, in this case, as we are seeking the integral of ax² e^-bx on [0, ∞), the integral is

2a/b³