Calculus Examples

$\int 3 t d t$

Step 1

Since $3$ is constant with respect to $t$ , move $3$ out of the integral.

$3 \int t d t$

Step 2

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

$3 (\frac{1}{2} t^{2} + C)$

Step 3

Simplify the answer.

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Step 3.1

Rewrite $3 (\frac{1}{2} t^{2} + C)$ as $3 (\frac{1}{2}) t^{2} + C$ .

$3 (\frac{1}{2}) t^{2} + C$

Step 3.2

Combine $3$ and $\frac{1}{2}$ .

$\frac{3}{2} t^{2} + C$