# Thread: integration by parts

1. ## integration by parts

Hello. As part of a question i have to integrate xe^(-x^2). I thought the easiest way to do this is by integration by parts however when i do it it seems to end up with horrible answers. I know this is quite simple but if anyone could help me here it would be good. thanks

2. I did it using substitution
firts, make a=-x^2
now, da=-2x dx

now the integral looks like:
-(1/2) [Integral] e^a da

and just integrate, with the answer being:
-(1/2) e^a + C

and substitute back

-(1/2) e^(-x^2) + C

I think that's about right.

PS. [Integra] is the integral sign

3. $\displaystyle \int x.e^{-x^2}~dx$

Hint: Substitute $\displaystyle u=-x^2$.

4. Originally Posted by enmascarado
I did it using substitution
firts, make a=-x^2
now, da=-2x dx

now the integral looks like:
-(1/2) [Integral] e^a da

and just integrate, with the answer being:
-(1/2) e^a + C

and substitute back

-(1/2) e^(-x^2) + C

I think that's about right.
Yes, it's right