Calculus Examples

$\int \frac{e^{t} - t}{2} d t$

Step 1

Since $\frac{1}{2}$ is constant with respect to $t$ , move $\frac{1}{2}$ out of the integral.

$\frac{1}{2} \int e^{t} - t d t$

Step 2

Split the single integral into multiple integrals.

$\frac{1}{2} (\int e^{t} d t + \int - t d t)$

Step 3

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

$\frac{1}{2} (e^{t} + C + \int - t d t)$

Step 4

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

$\frac{1}{2} (e^{t} + C - \int t d t)$

Step 5

By the Power Rule, the integral of $t$ with respect to $t$ is $\frac{1}{2} t^{2}$ .

$\frac{1}{2} (e^{t} + C - (\frac{1}{2} t^{2} + C))$

Step 6

Simplify.

$\frac{1}{2} (e^{t} - \frac{1}{2} t^{2}) + C$