# How do I find the indefinite integral of sin(3x)cos(3x)?

Aug 5, 2018

The answer is $= - \frac{1}{12} \cos \left(6 x\right) + C$

#### Explanation:

We know that

$\sin 2 x = 2 \sin x \cos x$

Therefore,

$\sin \left(3 x\right) \cos \left(3 x\right) = \frac{1}{2} \sin \left(6 x\right)$

So,

The integral is

$I = \int \sin \left(3 x\right) \cos \left(3 x\right) \mathrm{dx} = \frac{1}{2} \int \sin \left(6 x\right) \mathrm{dx}$

$= - \frac{1}{12} \cos \left(6 x\right) + C$