PLEASE HELP- trigonometric substitution

[maeveoneill]

I have been stuck on this question for soo long. I think it is just the latter end that I am messing upp on.
Anyways, the question is: Evaluate the integral: integral between sqrt of 2 and 2 of 1/ (t^3 (sqrt (t^2 -1)))

subsitution- x = sec 0, dx = sec0 tan0 d0
note 0 = theta

sqrt( t^2- 1^2) = sqrt (sec0^2 - 1) = sqrt(tan0^2) = tan0

integral sqrt2 -2 of 1/ (t^3 (sqrt (t^2 -1)))
= integral of sqrt 2 - 2 of sec0tan0/ seco^3tan0 d0
= integral of sqrt 2 - 2 of 1/ sec0^2

... then im stuck..

hopefully it wasnt to hard to read all that.. any help would be appreaciated

 

[galactus]

You have it so far. Good work.

\(\displaystyle \L\\\frac{1}{sec^{2}({\theta})}=cos^{2}({\theta})\)

Now, integrate. \(\displaystyle \L\\\int{cos^{2}({\theta})}d{\theta}\)