Question

Find an anti derivative (or integral) of the following function by the method of inspection:Cos 3x

Answer 1

The anti derivative of cos 3x is a function of x whose derivative is cos 3x.
It is known that,

$\frac{d}{dx}$(sin3x)=3cos3x

$\Rightarrow$ cos3x=$\frac{1}{3}\frac{d}{dx}(\sin3x)$

∴ cos 3x =$\frac{d}{dx}\bigg(\frac{1}{3} \sin3x\bigg)$

Therefore, the anti derivative of cos3x is $\frac{1}{3}$sin3x.