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b*(-Csc[(a*x)/2]^2/(8*a) - Log[Cos[(a*x)/2]]/(2*a) + Log[Sin[(a*x)/2]]/(2*a) + Sec[(a*x)/2]^2/(8*a))

Integrate[b*Csc[a*x]^3, x] ==
b*(-Csc[(a*x)/2]^2/(8*a) - Log[Cos[(a*x)/2]]/(2*a) + Log[Sin[(a*x)/2]]/(2*a) + Sec[(a*x)/2]^2/(8*a)) 

                    3
Integrate[b Csc[a x] , x] == 

        a x 2           a x             a x
   -Csc[---]    Log[Cos[---]]   Log[Sin[---]]
         2               2               2
b (---------- - ------------- + ------------- + 
      8 a            2 a             2 a
 
        a x 2
    Sec[---]
         2
    ---------)
       8 a
Time to compute: 0.01 second
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