Calculus Examples

$\frac{3}{x}$

Step 1

Write $\frac{3}{x}$ as a function.

$f (x) = \frac{3}{x}$

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.

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

Step 4

Since $3$ is constant with respect to $x$ , move $3$ out of the integral.

$3 \int \frac{1}{x} d x$

Step 5

The integral of $\frac{1}{x}$ with respect to $x$ is $\ln (| x |)$ .

$3 (\ln (| x |) + C)$

Step 6

Simplify.

$3 \ln (| x |) + C$

Step 7

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

$F (x) =$ $3 \ln (| x |) + C$