I have this question in a quiz for uni:
They show the exact same question in my lecture notes equalling:
1/2 e^x^2 + C , though im confused on how they get rid of the x in front: xe^x^2
any help would be appreciated
$\displaystyle \int dx \, xe^{x^2}$Originally Posted by sterps
Let $\displaystyle y = x^2$, then $\displaystyle dy = 2x dx$
Then
$\displaystyle \int dx \, xe^{x^2} = \int \frac{dy}{2}e^y$
$\displaystyle = \frac{1}{2}e^y + C = \frac{1}{2}e^{x^2} + C$
I don't know of a way to do this using integration by parts because $\displaystyle \int dx \, e^{x^2}$ can't be done exactly.
-Dan