Calculus Examples

$5 e^{x}$

Step 1

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

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

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.

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

Step 4

Since $5$ is constant with respect to $x$ , move $5$ out of the integral.

$5 \int e^{x} d x$

Step 5

The integral of $e^{x}$ with respect to $x$ is $e^{x}$ .

$5 (e^{x} + C)$

Step 6

Simplify.

$5 e^{x} + C$

Step 7

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

$F (x) =$ $5 e^{x} + C$