Find the Function f(x)=5^x

$f (x) = 5^{x}$

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

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

The integral of $5^{x}$ with respect to $x$ is $\frac{5^{x}}{\ln (5)}$ .

$\frac{5^{x}}{\ln (5)} + C$

Rewrite $\frac{5^{x}}{\ln (5)} + C$ as $\frac{1}{\ln (5)} \cdot 5^{x} + C$ .

$\frac{1}{\ln (5)} \cdot 5^{x} + C$

The function $F$ if derived from the integral of the derivative of the function. This is valid by the fundamental theorem of calculus.

$F (x) = \frac{1}{\ln (5)} \cdot 5^{x} + C$