Explicit integral could not be found

I try to evaluate following integral of:

   syms a b x
 >> f=1/(a - b*sin(x))

 f =

 1/(a - b*sin(x))

 >> assume(0 < a)
 >> assume(0 < b)
 >> assume(b < a)
 >> int(f, x,0,2*pi)
 Warning: Explicit integral could not be found. 

 ans =

 int(1/(a - b*sin(x)), x == 0..2*pi)

And i am getting a error but Mathematica solved this integral!!!!!!!!!!!!

Answer 1

[John BG]

try solving with a and be defined in advance:

   syms x
   f=1/(2-3*sin(x))
  f =
  -1/(3*sin(x) - 2)
   int(f,0,2*pi)
  ans =
  (2*5^(1/2)*limit(atanh((3*5^(1/2))/5 - (2*5^(1/2)*tan(x/2))/5), x, 2*atan(5^(1/2)/2 + 3/2), 'Left'))/5 - Inf

[mostafa kohe]

hi john The solution for a = 2 and b = 3, but not the parameters ( for all a and b). Meanwhile The question assumes that a> b

[mostafa kohe]

The correct answer is 2*pi / sqrt (a ^ 2 - b ^ 2), that calculated by MATHEMATICA