Calculus Examples

$\int (- \frac{3}{x} + 3 e^{x}) d x$

Step 1

Remove parentheses.

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

Step 2

Split the single integral into multiple integrals.

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

Step 3

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

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

Step 4

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

$- (3 \int \frac{1}{x} d x) + \int 3 e^{x} d x$

Step 5

Multiply $3$ by $- 1$ .

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

Step 6

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

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

Step 7

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

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

Step 8

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

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

Step 9

Simplify.

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