integrate xlnx/(square root x^2-1)

how i started:

by using integration by parts i got (lnx)(2/3(x^2-1)^(3/2) - integral 2/3(x^2-1)^(3/2)/(x)

where i let u= lnx v=2/3(x^2-1)^3/2

du= (1/x)dx dv= x(x^2-1)^-(1/2)dx

I dont how to take the integral of that function.