trig substitution integral

[disappoint]

im working on a trig substitution problem, and im a little stuck at this point
the problem is find the indefinite integral of dx/x(x^(2)-1)^(3/2) for x>1
what I've done so far is factored the denominator into x(x^2-1)((x^2-1)^(1/2))
at this point, i substituted x= sec t, so dx = sec t * tan t dt
and the integral becomes, sec t tan t dt / sec t tan^2 t tan t
after simplifying it works out to the indefinite integral of dt/tan^2 t, or cot^2 t dt
from here i used the trig identity cot ^2 t = csc ^2 t -1
and solved the integral in terms of t as -cot t -t + C
after substituting to get back to values for x, my answer was -1/sqrt(x^2-1) -arcsec x + C
however, the online program that my school uses for calculus homework says this is wrong... and ive checked the work a few times through and dont see another way to do it, unless im just making a stupid mistake somewhere that i havent noticed, or this answer is equivalent to another form that the online system likes better. id appreciate any suggestions anyone can offer, thanks in advance.

 

[galactus]

or this answer is equivalent to another form that the online system likes better

That could be. Your solution appears to be OK. These computer systems can be cantankerous.

You could try \(\displaystyle -tan^{-1}(\sqrt{x^{2}-1})-\frac{1}{\sqrt{x^{2}-1}}+C\)

This is the same thing only different

Also, try it without the C.