intergrating trig function?

Question

theta is the greek symbol often used to represent angles..

l = [ 2 / sin theta ] + [ 3 / cos theta]

when dl = O?

Answer 1

Let x = theta
I = ∫ 2 / sin x + 3 / cos x dx
I = ∫ (2.cosec x + 3.sec x).dx
I = 2.log(tan(x/2)) + 3.log (sec x + tan x) + c
(these integrals are listed in text books as being standard integrals for cosec x and sec x so we accept these as fact)

Answer 2

ans= 2 log(cosec(theta)-cot(theta)) - 3 log(sec(theta)+tan(theta))
its easy if u try u can easily get it