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a*((-8*Cot[b*x])/(15*b) - (4*Cot[b*x]*Csc[b*x]^2)/(15*b) - (Cot[b*x]*Csc[b*x]^4)/(5*b))

Integrate[a*Csc[b*x]^6, x] ==
a*((-8*Cot[b*x])/(15*b) - (4*Cot[b*x]*Csc[b*x]^2)/ (15*b) - (Cot[b*x]*Csc[b*x]^4)/(5*b)) 

                    6
Integrate[a Csc[b x] , x] == 

                                    2
   -8 Cot[b x]   4 Cot[b x] Csc[b x]
a (----------- - -------------------- - 
      15 b               15 b
 
                     4
    Cot[b x] Csc[b x]
    ------------------)
           5 b
Time to compute: 0.01 second
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