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## Homework Statement

Determine the length of the following graph:

[tex]f(x) \ = \ \frac{x^5}{10} + \frac{1}{6x^3}[/tex]

## Homework Equations

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

## The Attempt at a Solution

so [tex]f'(x) = \frac{x^4}{2} -\frac{1}{18x^4} [/tex]

[tex]f'(x)^2 = \frac{x^8}{4} + \frac{1}{18} + \frac{1}{324x^8}[/tex]

Is f'(x)^2 correct?

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