Calculus Examples

$\int [\frac{2}{x} + 3 e^{x}] d x$

Step 1

Remove parentheses.

$\int \frac{2}{x} + 3 e^{x} d x$

Step 2

Split the single integral into multiple integrals.

$\int \frac{2}{x} d x + \int 3 e^{x} d x$

Step 3

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

$2 \int \frac{1}{x} d x + \int 3 e^{x} d x$

Step 4

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

$2 (\ln (| x |) + C) + \int 3 e^{x} d x$

Step 5

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

$2 (\ln (| x |) + C) + 3 \int e^{x} d x$

Step 6

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

$2 (\ln (| x |) + C) + 3 (e^{x} + C)$

Step 7

Simplify.

$2 \ln (| x |) + 3 e^{x} + C$