# Evaluate the integral using subsitution rule int cos^3xsinx dx?

Jan 19, 2017

$\int {\cos}^{3} \left(x\right) \sin \left(x\right) \mathrm{dx} = \frac{- {\cos}^{4} \left(x\right)}{4} + C$

#### Explanation:

Let

$u = \cos \left(x\right)$

then

$\mathrm{du} = - \sin \left(x\right)$

Then we can write

$\int {\cos}^{3} \left(x\right) \sin \left(x\right) \mathrm{dx} = - \int {u}^{3} \mathrm{du} = - {u}^{4} / 4 + C$

Then by substituting $\cos \left(x\right)$ back in we get

$\underline{\int {\cos}^{3} \left(x\right) \sin \left(x\right) \mathrm{dx} = \frac{- {\cos}^{4} \left(x\right)}{4} + C}$