How to find the integral of (2cos x+3sin x)/(1+sin x) using the integral of dx/(1+sin x)(this is give below)

integral of dx/(1+sin x)= -2 / (tan (x/2) + 1
Thanks

∫ (2 cos x + 3 sin x) dx / (1 + sin x)
= ∫ [2 cos x/(1 + sin x) + 3 sin x/(1 + sin x)] dx
= ∫ [2 cos x/(1 + sin x) + 3 (1 + sin x - 1)/(1 + sin x)] dx
= ∫ [2 cos x/(1 + sin x) + 3 (1 - 1/(1 + sin x))] dx
= ∫ [2 cos x/(1 + sin x) + 3 - 3/(1 + sin x)] dx
= 2 ln |1 + sin x| + 3x - 3 * -2 / (tan(x/2) + 1) + C, using the hint above
= 2 ln |1 + sin x| + 3x + 6/(tan(x/2) + 1) + C.

I hope this helps!