# How do I find this integral?

1. Dec 24, 2017

### Math9999

1. The problem statement, all variables and given/known data
Find the integral of 1/(1+cosx) dx from -pi/2 to pi/2.

2. Relevant equations
None.

3. The attempt at a solution
Here's my work:
1/(1+cosx)=(1-cosx)/((1+cosx)(1-cosx))=(1-cosx)/(1-cos^2 x)=(1-cosx)/sin^2 x
This is what I've got so far. But this doesn't seem to simplify the integrand.

2. Dec 24, 2017

### PeroK

That looks good so far. What about splitting up the integral into two now?

3. Dec 24, 2017

### Math9999

Never mind. I got it. You gave me the big hint already, splitting it up.

4. Dec 24, 2017

### Math9999

Thank you so much! Merry Christmas!

5. Dec 24, 2017

### PeroK

There was a quicker way. Hint: $x = 2(x/2)$.

6. Dec 24, 2017

Wow.