Question

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

Answer 1

The anti derivative of $e^{2x}$ is the function of x whose derivative is $e^{2x}$ .
It is known that,

$\frac{d}{dx}(e^{2x})=2e^{2x}$

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

∴$e^{2x}= \frac{d}{dx}\bigg(\frac{1}{2}e^{2x}\bigg)$

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