Integral of tangent squared of x

[grief]

I tried and tried and I'm not able to solve this. I've managed to find the integral of sin squared of x by using the fact that cos(2x)=1-2(sin(x))^2, but I'm not able to do the same for tangent because I'm stuck with a quotient.

 

[Galileo]

Have you ever seen the term tan^2(x) in a derivative of some function? Recognizing this may put you on the right track.

 

[d_leet]

well since
1 + (tan(x))^2 = (sec(x))^2

and we know that the derivative of tan(x) is (sec(x))^2

then it's easy to find the integral of (tan(x))^2

 

[Hurkyl]

I've merged your two threads.

P.S.: What "quotient" did you get that you were having trouble integrating? If I could see it, maybe I could give a hint on how to integrate it.

P.P.S.: people learn better when you give them hints, or direction on the problem than when you do most of the steps for them and just leave a short blank at the end.

 

[grief]

never mind, I was on the wrong track. What d_leet said was right, you need to use (sec(x))^2

 

[Hurkyl]

never mind, I was on the wrong track.

I'm not so sure. You certainly weren't on the easy track, but I am not yet ready to believe you were on the wrong track.