Calculus Examples

$9 x^{4}$

Step 1

Write $9 x^{4}$ as a function.

$f (x) = 9 x^{4}$

Step 2

The function $F (x)$ can be found by finding the indefinite integral of the derivative $f (x)$ .

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

Step 3

Set up the integral to solve.

$F (x) = \int 9 x^{4} d x$

Step 4

Since $9$ is constant with respect to $x$ , move $9$ out of the integral.

$9 \int x^{4} d x$

Step 5

By the Power Rule, the integral of $x^{4}$ with respect to $x$ is $\frac{1}{5} x^{5}$ .

$9 (\frac{1}{5} x^{5} + C)$

Step 6

Simplify the answer.

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Step 6.1

Rewrite $9 (\frac{1}{5} x^{5} + C)$ as $9 (\frac{1}{5}) x^{5} + C$ .

$9 (\frac{1}{5}) x^{5} + C$

Step 6.2

Combine $9$ and $\frac{1}{5}$ .

$\frac{9}{5} x^{5} + C$

Step 7

The answer is the antiderivative of the function $f (x) = 9 x^{4}$ .

$F (x) =$ $\frac{9}{5} x^{5} + C$