What is the indefinite integral of the function cos^4x*sinx ?

To evaluate the integral of the function, we'll have to
use substitution method.

Let cos x = t
.

We'll differentiate both
sides:

-sin x dx = dt => sin x dx =
-dt

`int` (cos x)^4*sin x dx = - `int` t^4
dt

`int` - ` ` t^4 dt = - t^5/5 +
C

The indefinite integral of the function is
`int` (cos x)^4*sin x dx = -(cos x)^5/5 + C