Calculus Examples

$\int (t^{2} - \cos (t)) d t$

Step 1

Remove parentheses.

$\int t^{2} - \cos (t) d t$

Step 2

Split the single integral into multiple integrals.

$\int t^{2} d t + \int - \cos (t) d t$

Step 3

By the Power Rule, the integral of $t^{2}$ with respect to $t$ is $\frac{1}{3} t^{3}$ .

$\frac{1}{3} t^{3} + C + \int - \cos (t) d t$

Step 4

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

$\frac{1}{3} t^{3} + C - \int \cos (t) d t$

Step 5

The integral of $\cos (t)$ with respect to $t$ is $\sin (t)$ .

$\frac{1}{3} t^{3} + C - (\sin (t) + C)$

Step 6

Simplify.

$\frac{1}{3} t^{3} - \sin (t) + C$