You need to use the following substitution `cos theta = u` , such that:

`cos theta = u=> -sin theta d theta = du =>sin theta d theta = -du`

`int cos^4 theta*sin theta d theta = - int u^4 du`

`- int u^4 du = -(u^5)/5 + c`

Replacing back `cos theta` for` u` yields:

`int cos^4 theta*sin theta d theta = -((cos theta)^5)/5 + c`

**Hence, evaluating the indefinite integral, yields `int cos^4 theta*sin theta d theta = -((cos theta)^5)/5 + c` **