integration by parts

• Apr 1st 2008, 05:45 AM
studentsteve1202
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
• Apr 1st 2008, 06:14 AM
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

PS. [Integra] is the integral sign
• Apr 1st 2008, 06:15 AM
wingless
$\displaystyle \int x.e^{-x^2}~dx$

Hint: Substitute $\displaystyle u=-x^2$.
• Apr 1st 2008, 06:16 AM
wingless
Quote:

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