Integral of $$$4^{2 x}$$$

Find $$$\int 4^{2 x}\, dx$$$.

The input is rewritten: $$$\int{4^{2 x} d x}=\int{16^{x} d x}$$$.

Apply the exponential rule $$$\int{a^{x} d x} = \frac{a^{x}}{\ln{\left(a \right)}}$$$ with $$$a=16$$$:

$${\color{red}{\int{16^{x} d x}}} = {\color{red}{\frac{16^{x}}{\ln{\left(16 \right)}}}}$$

Therefore,

$$\int{16^{x} d x} = \frac{16^{x}}{\ln{\left(16 \right)}}$$

Simplify:

$$\int{16^{x} d x} = \frac{16^{x}}{4 \ln{\left(2 \right)}}$$

Add the constant of integration:

$$\int{16^{x} d x} = \frac{16^{x}}{4 \ln{\left(2 \right)}}+C$$

$$$\int 4^{2 x}\, dx = \frac{16^{x}}{4 \ln\left(2\right)} + C$$$A