# Integration question , Help

1. Dec 24, 2011

### Redoctober

1. The problem statement, all variables and given/known data
Determine the integral of the following

∫(1/(1+cos(x)).dx
∫(x+sin(x))/(1+cos(x)).dx

3. The attempt at a solution

I tried integration by parts and substution , but didn't work !
Help :/ !

2. Dec 24, 2011

### DivisionByZro

Show us what you've got. Here are hints:
1 - Use the identity that cos(x)=2*cos(x/2)-1, and then use a simple substitution.
2 - Somewhat similar to the first one.

3. Dec 24, 2011

### Redoctober

I got tan(x/2) + C for the first But nothin for the second .
i did as follows

∫(x+sin(x))/(x+cos(x)).dx

simplified it to

∫(x*sec^2(x)).dx + 2∫tan(x/2).dx

I then i integrated them , i used integration by parts for then right hand integral
Then i finally got
2x*tan(x/2)

Is it correct :D ?

4. Dec 24, 2011

### SammyS

Staff Emeritus
That identity should be
cos(x)=2*cos2(x/2)-1 .​

5. Dec 24, 2011

### SammyS

Staff Emeritus
The ∫(x*sec^2(x)).dx + 2∫tan(x/2).dx that you have should be: ∫(x*sec^2(x/2)).dx + 2∫tan(x/2).dx .

Yes, your answer is correct, if you add an arbitrary constant.

6. Dec 25, 2011

### Redoctober

Oh ok thanks :D ! i always forget the arbitrary unit lol xD