Question

what is the integration of 1 / 1 + sin x ??

Answer 1

I = dx/(1 + sinx)
= dx/{ 1 + cos(π/2 - x)
= dx/2sin²(π/4 -x/2)
[ using (1 +cos∅ ) 2sin²∅/2 ]
= 1/2 . Sec²(π/4 - x/2).dx
= 1/2 . tan( π/4 - x/2)/ (-1/2) + C
= - tan( π/4 - x/2) + C