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

⚠ 2e is read as the product 2*e: for a power, write 2^e‖2x is read as the product 2*x: for a power, write 2^x

Let's integrate:

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

For the math expression:

2 e^{(2 x)}

, we know the derivative formula:

\frac{d}{d x} (\exp (a)) = \exp (a)

, so we try differentiating with exp

Let's perform the differentiation:

\frac{d}{d x} (\exp (2 x))

We differentiate using:

\frac{d}{d x} (\exp (f)) = \frac{d}{d x} (f) \cdot \exp (f)

(where f =

2 x

)

\frac{d}{d 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)}

ℹ

\frac{2}{2}

1

‖

1 \cdot e^{(2 x)}

e^{(2 x)}

e^{(2 x)}

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

e^{(2 x)} + C