integrate the following?

Question

integral(1/(x^2(x^2-16)^.5))

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Answer 1

The most important step for this integration is to do a variable change x = 1/t, or t = 1/x, thus we have dx = d(1/t) = (-1/t^2)dt
[integral sign] dx/(x^2(x^2-16)^.5)
= [integral sign] - dt / ((1/t^2-16)^.5)
= [integral sign] - t dt / ((1 -16t^2)^.5)
= (1/32) [integral sign] d(1 -16t^2) / ((1 -16t^2)^.5)
= (1/16) (1 -16t^2)^.5 + C
= (1/16) {(x^2 -16)^.5}/x + C