Integrating x^2/((x^2-1)^(1/2))

[MathsNoobie]

Homework Equations

Need to integrate x^2/((x^2-1)^(1/2)).

The Attempt at a Solution

I first broke the equation into (x^2-1)^(1/2) + (x^2-1)^(-1/2)

Hence Integral (x^2/((x^2-1)^(1/2))) = Integral((x^2-1)^(1/2)) + Integral((x^2-1)^(-1/2)))


Further on Integral((x^2-1)^(1/2)) is an integral by parts.


Hence Integral((x^2-1)^(1/2)) = x(x^2-1)^(1/2) - Integral(x^2/((x^2-1)^(1/2)))

Therefore Integral (x^2/((x^2-1)^(1/2))) = 1/2(x(x^2-1)^(1/2) + Integral((x^2-1)^(-1/2))

But now I am stuck on how to solve the Integral((x^2-1)^(-1/2)).

I am sorry that I can't put this into Latex form as my name suggest I don't know how to use Latex.

 

[Dick]

I think it's time to try a trig substitution. How about x=sec(u)?