"Use the substitution x=secθ where 0<=θ<π/2 to evaluate
(integrand) √(x^2-1)/x^4 dx."
so after substitution:
⌠ 2
⎮ √(SEC(θ) - 1)
⎮ ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ dx
(it still should be dx right? not dθ?)
(**) you need to switch the dx over
⎮ 4
⌡ SEC(θ)
after using trig identities I get (sigma)(1-sin^2θ)sinθcosθdx
the I let u = sinθ and -du=cosθdx
so
⌠ 3
- ⌡ (u - u ) du
and that is -(u^2)/2+(u^4)/4 +C
I suspect this is where I mess things up.
and then I plug back in the value of u to get
-(sin^2θ)/2+(sin^4θ)/4+c
my CAS gives me SIN(θ)^2·(SIN(θ)^2 - 2)/4 but I don't think that's the same