Evaluate 
Multiplying numerator and denominator with 1-sinx
We get 
Taking 
and
Solving for A
Taking cos x=t
On differentiating both sides we get
-sin x dx=dt
Putting values in A we get our equation as
= t-1+c
Substituting value of t,
=sec x + c
Solving for B
= ∫ sec2x - ∫ 1 dx
= tan x – x +c
Final answer is A+B
= sec x + tan x – x + c
1