Calculus Examples

$\int (- \frac{1}{x} + 7 e^{x}) d x$

Step 1

Remove parentheses.

$\int - \frac{1}{x} + 7 e^{x} d x$

Step 2

Split the single integral into multiple integrals.

$\int - \frac{1}{x} d x + \int 7 e^{x} d x$

Step 3

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

$- \int \frac{1}{x} d x + \int 7 e^{x} d x$

Step 4

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

$- (\ln (| x |) + C) + \int 7 e^{x} d x$

Step 5

Since $7$ is constant with respect to $x$ , move $7$ out of the integral.

$- (\ln (| x |) + C) + 7 \int e^{x} d x$

Step 6

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

$- (\ln (| x |) + C) + 7 (e^{x} + C)$

Step 7

Simplify.

$- \ln (| x |) + 7 e^{x} + C$