Question

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

Answer 1

We are looking for a function whose derivative is $e^{2x}$
We recall,
$\frac{d}{dx}{e}^{2x}=2e^{2x}$
$\Rightarrow e^{2x}=\frac{1}{2}\frac{d}{dx}\left(e^{2x}\right)$
$\Rightarrow e^{2x}=\frac{d}{dx}\left(\frac{1}{2}{e}^{2x}\right)$

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