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I integrate by part I assume $dx=dv$ and $\ln(\sin x)= u$ or I compute by Maple but its answer wasn't clearly (Maple answer: xln(1-exp((2I)x))+xln(sin(x))+(1/2*I)x^2+(1/2*I)*polylog(2, e((2*I)*x))) thanks for any hints

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Your formatting has gone astray. Can you please correct? Regards – Amzoti Jan 16 '13 at 20:05
    
Do you have bounds? – NeverBeenHere Jan 16 '13 at 20:24
    
I pasted Integral(log(sin(x)),x) into wolframalpha.com to get a result. The solution contained something called polylogarithm. – miracle173 Jan 16 '13 at 20:34
    
whats polylogarithm ? how wolframalpha.com compute it? – Maisam Hedyelloo Jan 16 '13 at 20:41
    
wolframalpha.com – miracle173 Jan 16 '13 at 20:48

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