Calculus Examples

$f (x) = 2^{x}$

The function $F (x)$ can be found by finding the indefinite integral of the derivative $f (x)$ .

$F (x) = \int f (x) d x$

Set up the integral to solve.

$F (x) = \int 2^{x} d x$

The integral of $2^{x}$ with respect to $x$ is $\frac{2^{x}}{\ln (2)}$ .

$\frac{2^{x}}{\ln (2)} + C$

Rewrite $\frac{2^{x}}{\ln (2)} + C$ as $\frac{1}{\ln (2)} \cdot 2^{x} + C$ .

$\frac{1}{\ln (2)} \cdot 2^{x} + C$

The answer is the antiderivative of the function $f (x) = 2^{x}$ .

$F (x) =$ $\frac{1}{\ln (2)} \cdot 2^{x} + C$