Hey. Please help.
I have a differentiable function, $\displaystyle f$
Find $\displaystyle \int xf '(x^2) \, dx $
Thanks for the quick reply, Moo.
I'm probably being really silly, but I just can't finish it off.
Using $\displaystyle t = x^2 $
$\displaystyle \int \frac{t^{-\frac{1}{2}}}{2} f '(t) \, dt $
Using substitution by parts...
$\displaystyle \int \frac{t^{-\frac{1}{2}}}{2} f '(t) \, dt = \frac{t^{-\frac{1}{2}}}{2} f'(t) + \frac{1}{4} \int t^{-\frac{3}{2}} f(t) $
Any idea?
Thanks.
EDIT: Hang on for 5 mins, I think I've spotted my mistake.