# How do you integrate sin(x)cos(x)?

We have to fond the integral of sin x cos x

### Solution

To find the $\int \sin x\cos x$

We will use the given trigonometric identity

We know the identity

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

Substituting the identity in the given integral we get

$\int \sin x\cos x=\frac{1}{2}\int \sin 2x$

Let u = 2x and du=2dx

$\int \sin x\cos x=\frac{1}{4}\int \sin u . du$ $\int \sin x\cos x=-\frac{1}{4}\cos u + C$

$\int \sin x\cos x=-\frac{1}{4}\cos u + C$