integrate 2e^(2x) — step-by-step solution

Let's integrate:

\int(2 e^{(2 x)})dx

We attempt to reverse an integration: starting from

2 e^{(2 x)}

and

{(\exp (a))}^{'} = \exp (a)

, we differentiate using exp

Let's differentiate:

{(\exp (2 x))}^{'}

We differentiate using:

{(\exp (f))}^{'} = {(f)}^{'} \cdot \exp (f)

(where f =

2 x

)

{(2 x)}^{'} \cdot \exp (2 x)

2 \exp (2 x)

The computed derivative matches the original math expression up to a constant factor. Therefore, the integral is:

\frac{2}{2} \cdot e^{(2 x)}

e^{(2 x)}

Indefinite integrals are defined up to an additive constant C, so this yields:

e^{(2 x)} + C

▷Result: $e^{(2 x)} + C$ , with C being any constant