# Finding the length of a graph

## Homework Statement

Determine the length of the following graph:

$$f(x) \ = \ \frac{x^5}{10} + \frac{1}{6x^3}$$

## Homework Equations

length of a graph: $$\int \sqrt{1 + f'(x)^2}dx$$

## The Attempt at a Solution

so $$f'(x) = \frac{x^4}{2} -\frac{1}{18x^4}$$

$$f'(x)^2 = \frac{x^8}{4} + \frac{1}{18} + \frac{1}{324x^8}$$

Is f'(x)^2 correct?

Did I even need to expand, or is there some trick to this?

Dick