# Prove

Question:

Cos 3x

Solution:

The anti derivative of cos 3x is a function of x whose derivative is cos 3x.

It is known that,

$\frac{d}{d x}(\sin 3 x)=3 \cos 3 x$

$\Rightarrow \cos 3 x=\frac{1}{3} \frac{d}{d x}(\sin 3 x)$

$\therefore \cos 3 x=\frac{d}{d x}\left(\frac{1}{3} \sin 3 x\right)$

Therefore, the anti derivative of $\cos 3 x$ is $\frac{1}{3} \sin 3 x$.