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(-5*Cos[a*x])/(8*a) + (5*Cos[3*a*x])/(48*a) - Cos[5*a*x]/(80*a)

Integrate[Sin[a*x]^5, x] ==
(-5*Cos[a*x])/(8*a) + (5*Cos[3*a*x])/(48*a) - Cos[5*a*x]/(80*a) 

                  5
Integrate[Sin[a x] , x] == 

-5 Cos[a x]   5 Cos[3 a x]   Cos[5 a x]
----------- + ------------ - ----------
    8 a           48 a          80 a
Time to compute: < 0.01 second
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