yes u are right

my solution goes as

take  x^2-1=t

dx=dt/2x

substitute it ,get

[xlog |x|  /-t*t^1/2 ] dt/2x

-1/4log|t+1| / t^3/2 dt                         (x^2=1+t   =>  x=(t+1)^1/2)

now do it by parts and then put  t=tan^2@

and u will get the answer