INDEFINITE

âˆ«Sinxx=??

1 Answers

226

Abhas Agarwal ·2013-01-22 08:50:25

Since sin x = Î£(n = 0 to âˆž) (-1)^n x^(2n+1) / (2n+1)!,
sin x / x = Î£(n = 0 to âˆž) (-1)^n x^(2n) / (2n+1)!.

Integrating term by term yields
âˆ« sin x dx / x = Î£(n = 0 to âˆž) (-1)^n x^(2n+1) / [(2n+1) * (2n+1)!].

I hope this helps!

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