huh. You have the trig substitution. What's the problem?
If x = 2sec(t) then
dx = 2sec(t)tan(t) dt
Draw the triangle for t, and you can see that
√((x^2-4)/x) = sin(t)
Then
√((x^2-4)/x) dx = 2sec(t)tan(t)sin(t) dt = 2tan^2(t) dt = 2sec^2(t)-2 dt
That should be easy, right?
Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of integration.) ∫√((x^2-4)/x)dx
x=2sec(t)
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