Question

What is the antiderivative of $e^{2x}$?

Answer 1

Determining the antiderivative of $e^{2x}$.

The antiderivative of $e^{2x}$ is the function of $x$ whose derivative is $e^{2x}$ We know that,
$\frac{d}{dx}\left(e^{2x}\right)=2e^{2x}·dx$

Rearranging the terms we get

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

Hence, the antiderivative of $e^{2x}$ is "$\frac{d}{dx}\frac{1}{2}{e}^{2x}$" .