# How do you integrate  (x^(7))e^(x^(8)) dx?

Apr 17, 2015

$\int {x}^{7} {e}^{{x}^{8}} \mathrm{dx}$

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

Let $u = {x}^{8}$. This makes $\mathrm{du} = 8 {x}^{7} \mathrm{dx}$,

$\int {x}^{7} {e}^{{x}^{8}} \mathrm{dx} = \frac{1}{8} \int {e}^{{x}^{8}} \left(8 {x}^{7}\right) \mathrm{dx} = \frac{1}{8} \int {e}^{u} \mathrm{du}$

$= \frac{1}{8} {e}^{u} + C = \frac{1}{8} {e}^{{x}^{8}} + C$

(Check by differentiating $\frac{1}{8} {e}^{{x}^{8}} + C$)

Apr 17, 2015

STEP 1:

STEP 2: