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

The calculator will find the integral/antiderivative of $$$4^{x}$$$, with steps shown.

Related calculator: Definite and Improper Integral Calculator

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


Apply the exponential rule $$$\int{a^{x} d x} = \frac{a^{x}}{\ln{\left(a \right)}}$$$ with $$$a=4$$$:

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


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


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

Add the constant of integration:

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

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