Find an anti derivative (or integral) of function by the method o… - Vidyadip

Question

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

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Answer

We know that
$\frac{d}{d x}\left(e^{2 x}\right)=2 e^{2 x}$
$\Rightarrow \mathrm{e}^{2 \mathrm{x}}=\frac{1}{2} \frac{d}{d x}\left(e^{2 x}\right)$
$=\frac{d}{d x}\left(\frac{1}{2} e^{2 x}\right)$
Therefore, the anti-derivative of $e^{2x}$ is $\frac{1}{2} e^{2 x}$.

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