`int cos^3(theta) sin(theta) d theta, u = cos(theta)` Evaluate the integral by making the given substitution.

You need to evaluate the indefinite integral by performing the substitution `u =cos theta` , such that:

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

`int cos^3 theta*sin theta*d theta = - int u^3 du`

Using the formula `int u^n du = (u^(n+1))/(n+1) + c` yields

`- int u^3 du = -(u^(3+1))/(3+1) + c`

`- int u^3 du = -(u^4)/4 + c`

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

`int cos^3 theta*sin theta*d theta =  -(cos^4 theta)/4 + c`

Hence, evaluating the indefinite integral yields `int cos^3 theta*sin theta*d theta =  -(cos^4 theta)/4 + c.`