Check the formula you used and than the integration you performed Is it correct
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.