Calculus Examples

$\int (\frac{5}{x} + e^{x}) d x$

Step 1

Remove parentheses.

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

Step 2

Split the single integral into multiple integrals.

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

Step 3

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

$5 \int \frac{1}{x} d x + \int e^{x} d x$

Step 4

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

$5 (\ln (| x |) + C) + \int e^{x} d x$

Step 5

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

$5 (\ln (| x |) + C) + e^{x} + C$

Step 6

Simplify.

$5 \ln (| x |) + e^{x} + C$