Oh OK. Then your first attempt was correct. You should be more clear what it is you're asking, as it was written it wasn't obvious you were integrating the expressions.
For future reference, if you just want to check your answers, try: http://www.wolframalpha.com . Just type in integrate 'expression' and press enter.
Sorry, but I originally assumed you had done the integral yourself in two diferent ways and arrived at different answers and wanted to check which was correct.
Have you done integration by substitution before?
Try working through setting
Do you know how to differentiate to get ? I already gave you the answer to this part in my previous post.
Having done that simply substitute everything in.
Post some working and let me know exactly where you get stuck.
I'm going out now so won't be able to reply again, if you're still stuck use the link I gave you. type in 'integrate (2 sec(x) / (2 + tan(x)))^2' and the press enter. When it gives you the answer click on more steps.