# 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
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
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.