# How do you integrate x^4 e^x^5 dx?

Apr 17, 2015

$\int {x}^{4} {e}^{{x}^{5}} \mathrm{dx}$

Use substitution to write this an an integral of ${e}^{u} \mathrm{du}$

Let $u = {x}^{5}$. This makes $\mathrm{du} = 5 {x}^{4} \mathrm{dx}$,

$\int {x}^{4} {e}^{{x}^{5}} \mathrm{dx} = \frac{1}{5} \int {e}^{{x}^{5}} \left(5 {x}^{4}\right) \mathrm{dx} = \frac{1}{5} \int {e}^{u} \mathrm{du}$

$= \frac{1}{5} {e}^{u} + C = \frac{1}{5} {e}^{{x}^{5}} + C$

(Check by differentiating $\frac{1}{5} {e}^{{x}^{5}} + C$)