# Thread: integration by parts - e^-x

1. ## integration by parts - e^-x

how does the first underlined part become the second..

does the.. x e^x-1 cancel? where does the -2 come from?

Help. Thankss

2. Nothing cancels, it's from filling in the boundaries.

$\displaystyle \left[-(x^2+1)e^{-x}\right]^{1}_{0}=\left(-(1^2+1)e^{-1}\right)-\left(-(0^2+1)e^{0}\right) = -2e^{-1}+1$

3. Originally Posted by calculus0
how does the first underlined part become the second..

does the.. x e^x-1 cancel? where does the -2 come from?

Help. Thankss
Dear calculus0,

$\displaystyle \left[-(x^{2}+1)e^{-x}\right]_{0}^{1}=\left[-(1^{2}+1)e^{-1}\right]-\left[-(0^{2}+1)e^{-0}\right]=-2e^{-1}+1$