Integral

**Anaturtle** · December 18th 2007, 02:29 PM

Could someone helpme?

I want to solve:

integral((e^sinx)/sinx)dx= ?

Thank you!

**Krizalid** · December 18th 2007, 02:47 PM

It's like integrating $\frac{e^x}x.$

There's no elementary primitive.

**Anaturtle** · December 18th 2007, 03:00 PM

Thank you. Can you provide the details to solve it?

thanks

**Krizalid** · December 18th 2007, 03:04 PM

$e^x = \sum\limits_{k = 0}^\infty {\frac{{x^k }}<br /> {{k!}}} \implies \frac{{e^x }}<br /> {x} = \sum\limits_{k = 0}^\infty {\frac{{x^{k - 1} }}<br /> {{k!}}} .$

You can interchange the integral by the sum, but it's not worth.

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