Calculus Examples

$2 x^{2}$

Step 1

Since $2$ is constant with respect to $x$ , move $2$ out of the integral.

$2 \int x^{2} d x$

Step 2

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

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

Step 3

Simplify the answer.

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Step 3.1

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

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

Step 3.2

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

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