Integral of e^sinx

Date: 15 May 1995 07:43:54 -0400
From: MUHTAR
Subject: problem
     
          INTEGRAL  e^sinx?

Date: 16 May 1995 22:28:59 -0400
From: Dr. Sydney
Subject: Re: problem

Hello!

Thanks for writing us!  This is a good question.  Certainly taking the
integral of e to the power sinx defies all of the usual tricks of
integration like substitution, parts, etc.  

I looked in a book of integrals and I saw nothing that looked even close to
this integral, so my guess is that there is no nice, pat answer to this
question.  Have you considered approximating the function to a Taylor
polynomial and integrating the Taylor polynomial?  At least locally (around
the number you do your expansion about), the integral should approximate the
integral of e^sinx  (If you don't know what Taylor polynomials are, write
back, and we'll be happy to help explain!).  

So, I hope this helps a little.  The problem would have worked much more
nicely if it were, say integral of cosx * e^sinx.  But, life isn't always
that simple, I guess.  Write back if you have any more questions.

--Sydney, "dr. Math"