Calculus Examples

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

Step 1

Write $\frac{1}{x} d x$ as a function.

$f (x) = \frac{1}{x} d x$

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.

$F (x) = \int \frac{1}{x} \cdot (d x) d x$

Step 4

Simplify.

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Step 4.1

Combine $d$ and $\frac{1}{x}$ .

$\int \frac{d}{x} \cdot x d x$

Step 4.2

Combine $\frac{d}{x}$ and $x$ .

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

Step 4.3

Cancel the common factor of $x$ .

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Step 4.3.1

Cancel the common factor.

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

Step 4.3.2

Divide $d$ by $1$ .

$\int d d x$

Step 5

Apply the constant rule.

$d x + C$

Step 6

The answer is the antiderivative of the function $f (x) = \frac{1}{x} \cdot (d x)$ .

$F (x) =$ $d x + C$