Q

Find an anti derivative (or integral) of the following functions by the method of inspection. e ^ 2x

Q3  Find an anti derivative (or integral) of the following functions by the method of inspection.  $e ^{2x}$

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GIven $e ^{2x}$;

So, the anti derivative of $e ^{2x}$ is a function of x whose derivative is $e ^{2x}$.

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

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

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

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

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