# How do you integrate (x^3)(e^(x^2))dx?

Apr 12, 2015

$\frac{1}{2} \left({x}^{2} {e}^{{x}^{2}} - {e}^{{x}^{2}}\right) + C$

#### Explanation:

Use substitution method by considering ${x}^{2} = u$, so that it is $x \setminus \mathrm{dx} = \frac{1}{2} \setminus \mathrm{du}$.

The given integral is thus transformed to $\frac{1}{2} u {e}^{u} \setminus \mathrm{du}$. Now integrate it by parts to have $\frac{1}{2} \left(u {e}^{u} - {e}^{u}\right) + C$.

Now substitute back ${x}^{2}$ for u, to have the Integral as

$\frac{1}{2} \left({x}^{2} {e}^{{x}^{2}} - {e}^{{x}^{2}}\right) + C$