INtegration by substitution followed by parts:

Well, what have you tried? This is clearly homework! Try writing tanx in terms of sinx and cosx.

 

this is by-parts integration because you have two functions multiplied by each other.
But before you do that you should use a trig identity (think of an identity which will give you an easily integratable trig function).

 

Bruk, please read the PF guidelines here: https://www.physicsforums.com/showthread.php?t=5374, paying particular attention to the part re giving complete solutions to homework/textbook style questions.

 

Good work though :P

 

Hint: Do you know an identity for tan²x in terms of, say, sec²x?

Try using this then integrate by parts. Post your work so we can help you.