I am having the hardest time trying to integrate the following problem.

$\displaystyle

\int\left[sec(x)*tan(x)\right]dx

$

I have tried writing the problem using sines and cosines but that did not help me. In my book it says the integral of this problem is sec(x), but I cannot get it.My book also gives me tips on how to integrate this problem when it sec(x) and tan(x) are raised to powers greater than one. If anyone can help me out I would greatly appreciate it.