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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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