Calculus Examples

\int 2 x^{2} d x

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

Step 1

Since

2

$2$ is constant with respect to

x

$x$ , move

2

$2$ out of the integral.

2 \int x^{2} d x

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

Step 2

By the Power Rule, the integral of

x^{2}

$x^{2}$ with respect to

x

$x$ is

\frac{1}{3} x^{3}

$\frac{1}{3} x^{3}$ .

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

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

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Rewrite

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

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

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

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

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

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

Step 3.2

Combine

2

$2$ and

\frac{1}{3}

$\frac{1}{3}$ .

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

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

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

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

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$