# Sec(x)tan(x) integral

1. Jan 27, 2014

### PauloE

1. The problem statement, all variables and given/known data
$∫sec(x)tan(x)+x/(x^2+1) dx$

3. The attempt at a solution
I replaced sec and tan by $1/cos(x)$ and $sin/cos(x)$ then end up with $sin(x)/cos^2(x)$
then I replace $cos^2 x$ by $1-sin^2 x$ then I dont know where to go.

the second part of the equation works with u substitution.
I just cant see where the identities of the first part are leading me.

2. Jan 27, 2014

### Curious3141

No, don't do that. Try the sub $u = \cos x$ and watch that sucker fold.

3. Jan 29, 2014

### PauloE

you know i just used tan(x) in the first term and u substitution in the second and it worked too!

Thanks a lot!
Paulo

4. Jan 29, 2014

### vela

Staff Emeritus
You should ideally recognize the derivative of sec x.

5. Jan 30, 2014

### utkarshakash

For the first integral you don't have to substitute anything. It is the derivative of sec(x).