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## Homework Statement

[2

^{3/4}, 2] 4/(x√(x

^{4}-4))

## Homework Equations

∫ du/(u√(u

^{2}- a

^{2})) = 1/a(sec

^{-1}(u/a) + c

## The Attempt at a Solution

I first multiplied the whole thing by x/x. This made the problem:

4x/(x

^{2}√(x

^{4}- 4))

Then I did a u substitution making u = x

^{2}. Therefore, du = 2xdx. I multiplied by 2 to get 2du = 4xdx

The problem then becomes 2∫du/(u√(u

^{2}- 4))

Solving the integral I got 2[(1/2)sec

^{-1}(x

^{2}/2)] from [2

^{3/4}, 2]

I plug in the bounds and get 2[(1/2)sec

^{-1}(2) - (1/2)sec

^{-1}(2

^{6/4}/2)

This is where I'm lost. The second sec does not seem like a nice number and I'm assuming my professor would make the problem come out nicely as he always has. I'm pretty sure I made a mistake somewhere because of this but I don't know where.[/B]