# Integration problem with e (check my work)

## Homework Statement

(integrate)5e^(5x)*sin(e^(5x))dx

## The Attempt at a Solution

I factored 5 out of the integration and made u to be e^5x, and du to be 5e^5x, or (1/5)du=e^(5x)dx. Because of this, the 5 factored out of the equation canceled out with the (1/5), leaving (integrate)u*sin(u).

I integrated that, making sin(u)-u*cos(u) (I think) and pu the e^(5x)s back where the u's were. Am I right in doing this?

$$\int{f'(x)\sin{f(x)} dx = -cos(f(x)) + C$$