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(x*(-Cos[Log[x]] + Sin[Log[x]]))/2

Integrate[Sin[Log[x]], x] ==
(x*(-Cos[Log[x]] + Sin[Log[x]]))/2 

Integrate[Sin[Log[x]], x] == 

x (-Cos[Log[x]] + Sin[Log[x]])
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              2
Time to compute: < 0.01 second
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