Hello everyone,

I was reading something and the following equation turns up:

$\displaystyle \int^T_0 e^{-rT}(T-t)dt $ =$\displaystyle \frac{rT+e^{-rT}-1}{r^2}$

Where r is a constant. It has been a while since I last did integrals. When I tried to work it out I ended up with (expand the bracket and then integrate each term)

$\displaystyle \frac{e^{-rT}T^2}{2}$

I am fully willing to admit that I have made a stupid mistake somewhere as it has been a long time from when I last tried to solve one.

Thank you for any help!