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

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

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

                                                2
   -8 Cot[a + b x]   4 Cot[a + b x] Csc[a + b x]
a (--------------- - ---------------------------- - 
        15 b                     15 b
 
                             4
    Cot[a + b x] Csc[a + b x]
    --------------------------)
               5 b
Time to compute: 0.04 second
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