Calculus Examples

x^{3}

$x^{3}$

Step 1

Write

x^{3}

$x^{3}$ as a function.

f (x) = x^{3}

$f (x) = x^{3}$

Step 2

The function

F (x)

$F (x)$ can be found by finding the indefinite integral of the derivative

f (x)

$f (x)$ .

F (x) = \int f (x) d x

$F (x) = \int f (x) d x$

Step 3

Set up the integral to solve.

F (x) = \int x^{3} d x

$F (x) = \int x^{3} d x$

Step 4

By the Power Rule, the integral of

x^{3}

$x^{3}$ with respect to

x

$x$ is

\frac{1}{4} x^{4}

$\frac{1}{4} x^{4}$ .

\frac{1}{4} x^{4} + C

$\frac{1}{4} x^{4} + C$

Step 5

The answer is the antiderivative of the function

f (x) = x^{3}

$f (x) = x^{3}$ .

F (x) =

$F (x) =$

\frac{1}{4} x^{4} + C

$\frac{1}{4} x^{4} + C$