Calculus Examples

$\int (5 e^{x} - \frac{2}{x}) d x$

Step 1

Remove parentheses.

$\int 5 e^{x} - \frac{2}{x} d x$

Step 2

Split the single integral into multiple integrals.

$\int 5 e^{x} d x + \int - \frac{2}{x} d x$

Step 3

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

$5 \int e^{x} d x + \int - \frac{2}{x} d x$

Step 4

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

$5 (e^{x} + C) + \int - \frac{2}{x} d x$

Step 5

Since $- 1$ is constant with respect to $x$ , move $- 1$ out of the integral.

$5 (e^{x} + C) - \int \frac{2}{x} d x$

Step 6

Since $2$ is constant with respect to $x$ , move $2$ out of the integral.

$5 (e^{x} + C) - (2 \int \frac{1}{x} d x)$

Step 7

Multiply $2$ by $- 1$ .

$5 (e^{x} + C) - 2 \int \frac{1}{x} d x$

Step 8

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

$5 (e^{x} + C) - 2 (\ln (| x |) + C)$

Step 9

Simplify.

$5 e^{x} - 2 \ln (| x |) + C$