Question

How do you find the integral of `int 1/(1 + cos(x))`?

Answer 1

`-cotx+cscx+"C"`

Explanation:

`int1/(1+cosx)dx = int(1-cosx)/((1+cosx)(1-cosx))dx`

`= int(1-cosx)/(1-cos^2x)dx`

`= int(1-cosx)/sin^2xdx`

`= int 1/sin^2xdx-intcosx/sin^2xdx`

=`int csc^2xdx-intcotxcscxdx`

=`-cotx+cscx+"C"`