Compute:

Integral(2*x^3*e^(-x^2))

For some reason I make a mistake with the minus-sign, I don't see where. We substitute:

u = x^2

=>

du/dx = 2x

=>

dx = du/2x

Thus we can write the integral as:

Integral(u*e^(-u))

Using integration by parts yields:

-u * e^(-u) - (-1*e^(-u)) = (1-u)*e^(-u)

But my calculator says -(1+u) - what am I doing wrong?