Question

Find Integration of
∫e^(2x)dx
Please give ans as fast as possible.​

Answer 1

$\displaystyle \int {e}^{2x} dx$

Let , 2x = t

$\implies2x \: = t$

$\implies2 \: dx \: = dt$

$\implies\: dx\: = \dfrac{dt}{2}$

Now put dx = dt/2 :-

$\implies\displaystyle \int {e}^{2x} dx = \displaystyle \int {e}^{t} \frac{dt}{2}$

$\implies \displaystyle \int {e}^{t} \frac{dt}{2}$

$\implies \dfrac{1}{2} \displaystyle \int {e}^{t} {dt}$

$\implies \dfrac{1}{2} {e}^{t} + c$

where c is constant.

$\implies \dfrac{{e}^{t}}{2} + c$

Now put 2x= t :-

$\implies \dfrac{ {e}^{2x} }{2} + c$

Answer :

$\dfrac{ {e}^{2x} }{2} + c$

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