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## Homework Statement

The integral of (x^n)(e^(-a*x^2)) is easier to evaluate when n is odd.

a) Evaluate ∫(x*e^(-a*x^2)*dx) (No computation allowed!)

b) Evaluate the indefinite integral of x*e^(-a*x^2), using a simple substitution.

c) Evaluate ∫(x*e^(-a*x^2)*dx) [from o to +inf]

d) Differentiate the previous result to evaluate ∫((x^3)(e^(-a*x^2))dx)

## Homework Equations

∫(e^(-a*x^2)*dx) = (1/2)√(∏/a)

## The Attempt at a Solution

I thought that the easiest solution might be using integration by parts, but I ran into the issue of the range being different on the integrals, and I have no idea how else I can do this unless I can assume that the function is even...

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