The integral 1/(sqrt((x^2)-9)

so far I have this....

x = 3sec(t)

dx = 3sec(t)tan(t)dt

this gives me --> integral (3sec(t)tan(t))dt/9(tan^2)(t)

1/3 integral sec(t)dt/tan(t) --> 1/3 integral csc(t)dt

1/3(-csc(t)cot(t)) + C = 1/3( -x/(sqrt(x^2 - 9)) * 3/(sqrt(x^2 - 9))

Please any help would be much appreciated!!! I don't know if I messed up or something. Any ideas?