Question

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

Answer 1

Apply the following substitution

`u=tan(x/2)` hence `dx=2/(1+u^2)du` , `sinx=(2u)/(1+u^2)`

hence you get the integral

`int 1/(1+sinx)dx=int 2/(u+1)^2du=-2/(1+u)+c=-2/(1+tan(x/2))+c`