Calculus Examples

$3^{x}$

Step 1

Write $3^{x}$ as a function.

$f (x) = 3^{x}$

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.

$F (x) = \int 3^{x} d x$

Step 4

The integral of $3^{x}$ with respect to $x$ is $\frac{3^{x}}{\ln (3)}$ .

$\frac{3^{x}}{\ln (3)} + C$

Step 5

Rewrite $\frac{3^{x}}{\ln (3)} + C$ as $\frac{1}{\ln (3)} \cdot 3^{x} + C$ .

$\frac{1}{\ln (3)} \cdot 3^{x} + C$

Step 6

The answer is the antiderivative of the function $f (x) = 3^{x}$ .

$F (x) =$ $\frac{1}{\ln (3)} \cdot 3^{x} + C$