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How do I integrate $$\int\frac{\sin(x)}xdx$$? I tried using integration by parts, but it led me to nowhere. Please help.

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    You have to use the (nonelementary) [sine integral](http://mathworld.wolfram.com/SineIntegral.html) in the general case; however, if you're interested in the limit from 0 to $\infty$, there is an m.SE question devoted to that topic...2011-05-05

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