how do i intergrate:
int(e^x(sqrt(1+e^x))) u=1+e^x
and
int((x^2)(e^x))
$\displaystyle \int \sqrt{u}\, du = \int u^{1/2} \, du = \frac{2}{3} u^{3/2} + C = \frac{2}{3} u\, u^{1/2} + C = \frac{2}{3} u \, \sqrt{u} + C$.
Now substitute back u = 1 + e^x.
I have no idea what you've done. The working you've done leading to your answer would no doubt reveal your error(s).