Calculus Examples

$5^{x}$

Step 1

Write $5^{x}$ as a function.

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

Step 2

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

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

Step 3

Set up the integral to solve.

$F (x) = \int 5^{x} d x$

Step 4

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

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

Step 5

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

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

Step 6

The answer is the antiderivative of the function $f (x) = 5^{x}$ .

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