Hi, I am trying to integrate this function, but do not know how to go past

$\displaystyle \int_{\theta}^{\infty}xe^{-(x-\theta)}dx $

Let $\displaystyle u = x, dv=e^{-(x-\theta)}, du = dx, v=-e^{-(x-\theta)} $

Therefore,

$\displaystyle -xe^{-(x-\theta)}\bigg|_{\theta}^{\infty}-\int_{\theta}^{\infty}-e^{-(x-\theta)} $

$\displaystyle [\underbrace{-xe^{-\infty}}_{0}+xe^{-(\theta-\theta)}]-[e^{-x-\theta}\bigg|_{\theta}^{\infty}] $

The X will not cancel, and I know that the answer, through Maple, is $\displaystyle 1+\theta $.

The command I used in maple is Code:

int(x*exp(-(x-theta)),x=theta..infinity);

. Perhaps I have done this incorrect.

Thank you!