Calculus Examples

$\frac{x + 1}{x}$

Step 1

Split the fraction into multiple fractions.

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

Step 2

Split the single integral into multiple integrals.

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

Step 3

Cancel the common factor of $x$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

Apply the constant rule.

$x + C + \int \frac{1}{x} d x$

Step 5

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

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

Step 6

Simplify.

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