Calculus Examples

$9 x^{- 8}$

Step 1

Write $9 x^{- 8}$ as a function.

$f (x) = 9 x^{- 8}$

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.

$F (x) = \int 9 x^{- 8} d x$

Step 4

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

$9 \int x^{- 8} d x$

Step 5

By the Power Rule, the integral of $x^{- 8}$ with respect to $x$ is $- \frac{1}{7} x^{- 7}$ .

$9 (- \frac{1}{7} x^{- 7} + C)$

Step 6

Simplify the answer.

Tap for more steps...

Step 6.1

Simplify.

Tap for more steps...

Step 6.1.1

Combine $x^{- 7}$ and $\frac{1}{7}$ .

$9 (- \frac{x^{- 7}}{7} + C)$

Step 6.1.2

Move $x^{- 7}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$9 (- \frac{1}{7 x^{7}} + C)$

Step 6.2

Simplify.

$9 (- \frac{1}{7 x^{7}}) + C$

Step 6.3

Simplify.

Tap for more steps...

Step 6.3.1

Multiply $- 1$ by $9$ .

$- 9 \frac{1}{7 x^{7}} + C$

Step 6.3.2

Combine $- 9$ and $\frac{1}{7 x^{7}}$ .

$\frac{- 9}{7 x^{7}} + C$

Step 6.3.3

Move the negative in front of the fraction.

$- \frac{9}{7 x^{7}} + C$

Step 7

The answer is the antiderivative of the function $f (x) = 9 x^{- 8}$ .

$F (x) =$ $- \frac{9}{7 x^{7}} + C$