Antiderivative question?

Question

What is..

int(1/[(x^2)*(sqrt(x^2-9))])dx

Answer 1

Substitute u = 1/x, so du = -(1/x^2)dx

the integral becomes that of int (u/√{1 - 9u^2})du

which is 1/9(1 - 9u^2)^0.5 which leads to
(x^2 - 9)^0.5/(9x) + a constant

Answer 2

How say a substitution u= V(x^2 - 9) then, du/dx = x / V(x^2 - 9)
is that x^2x in the denominator? then the integral is,
int. (u^2 +9)^ [V(u^2 +9) - (1/2)] dx

Tricky...I have a feeling logs may be involved by the look of that exponent.
Of course it may be multiplication and not x there and I'd just be silly.
Hope this helps!