Calculus Examples

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

Step 1

Remove parentheses.

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

Step 2

Split the single integral into multiple integrals.

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

Step 3

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

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

Step 4

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

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

Step 5

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

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

Step 6

Simplify.

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Step 6.1

Simplify.

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

Step 6.2

Simplify.

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Step 6.2.1

Multiply $- 1$ by $- 1$ .

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

Step 6.2.2

Multiply $\cos (t)$ by $1$ .

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