# How do I find this integral?

Math9999

## Homework Statement

Find the integral of 1/(1+cosx) dx from -pi/2 to pi/2.

None.

## 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.

PeroK
Science Advisor
Homework Helper
Gold Member
2020 Award

## Homework Statement

Find the integral of 1/(1+cosx) dx from -pi/2 to pi/2.

None.

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

• Math9999
Math9999
Never mind. I got it. You gave me the big hint already, splitting it up.

Math9999
Thank you so much! Merry Christmas!

PeroK
Science Advisor
Homework Helper
Gold Member
2020 Award
Never mind. I got it. You gave me the big hint already, splitting it up.
There was a quicker way. Hint: ##x = 2(x/2)##.

Math9999
Wow.