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x + (4*Cot[a*x])/(3*a) - (Cot[a*x]*Csc[a*x]^2)/(3*a)

Integrate[Cot[a*x]^4, x] ==
x + (4*Cot[a*x])/(3*a) - (Cot[a*x]*Csc[a*x]^2)/(3*a) 

                  4
Integrate[Cot[a x] , x] == 

                                  2
    4 Cot[a x]   Cot[a x] Csc[a x]
x + ---------- - ------------------
       3 a              3 a
Time to compute: 0.01 second
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