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Integrate[Sin[x]^12, x] ==
(231*x)/1024 - (99*Sin[2*x])/512 + (495*Sin[4*x])/8192 - (55*Sin[6*x])/3072 + (33*Sin[8*x])/8192 - (3*Sin[10*x])/5120 + Sin[12*x]/24576 

                12
Integrate[Sin[x]  , x] == 

231 x   99 Sin[2 x]   495 Sin[4 x]   55 Sin[6 x]
----- - ----------- + ------------ - ----------- + 
1024        512           8192          3072
 
  33 Sin[8 x]   3 Sin[10 x]   Sin[12 x]
  ----------- - ----------- + ---------
     8192          5120         24576
Time to compute: < 0.01 second
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