Calculus Examples

$(\int e^{x} - \frac{1}{9 x} d x) d x$

Step 1

Split the single integral into multiple integrals.

$(\int e^{x} d x + \int - \frac{1}{9 x} d x) d x$

Step 2

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

$(e^{x} + C + \int - \frac{1}{9 x} d x) d x$

Step 3

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

$(e^{x} + C - \int \frac{1}{9 x} d x) d x$

Step 4

Since $\frac{1}{9}$ is constant with respect to $x$ , move $\frac{1}{9}$ out of the integral.

$(e^{x} + C - (\frac{1}{9} \int \frac{1}{x} d x)) d x$

Step 5

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

$(e^{x} + C - \frac{1}{9} (\ln (| x |) + C)) d x$

Step 6

Simplify.

$(e^{x} - \frac{1}{9} \ln (| x |)) d x + C$