Question

Find an anti-derivative (or integral) of $\cos 3x$ by the method of inspection.

Answer 1

We are looking for a function whose derivative is $\cos 3x$
We recall
$\frac{d}{dx}\sin 3x=3\cos 3x$
$\Rightarrow \cos 3x=\frac{1}{3}\frac{d}{dx}\left(\sin 3x\right)$
$\Rightarrow \cos 3x=\frac{d}{dx}\left(\frac{1}{3}\sin 3x\right)$

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