Question

Find an anti derivative (or integral) of the given function by the method of inspection. $e^{2x}$

Answer 1

We know that,
$\frac{d}{dx}\left(e^{2x}\right)=2e^{2x}$

$\Rightarrow e^{2x}=\frac{1}{2}\frac{d}{dx}\left(e^{2x}\right)$

$\therefore e^{2x}=\frac{d}{dx}\left(\frac{1}{2}{e}^{2x}\right)$

Therefore, the anti derivative of $e^{2x}$ is $\frac{1}{2}{e}^{2x}$.