# 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
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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