Calculus Examples

$\int (e^{t} + \frac{1}{t}) d t$

Step 1

Remove parentheses.

$\int e^{t} + \frac{1}{t} d t$

Step 2

Split the single integral into multiple integrals.

$\int e^{t} d t + \int \frac{1}{t} d t$

Step 3

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

$e^{t} + C + \int \frac{1}{t} d t$

Step 4

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

$e^{t} + C + \ln (| t |) + C$

Step 5

Simplify.

$e^{t} + \ln (| t |) + C$