# How do you find the antiderivative of int (xe^(x^2)) dx?

$\int \left(x {e}^{{x}^{2}}\right) \mathrm{dx} = \frac{1}{2} {e}^{{x}^{2}} + C$
now $\frac{d}{\mathrm{dx}} \left({e}^{{x}^{2}}\right) = 2 x {e}^{{x}^{2}}$
$\int \left(x {e}^{{x}^{2}}\right) \mathrm{dx} = \frac{1}{2} {e}^{{x}^{2}} + C$