Groups > comp.soft-sys.math.maple > #1124

Elementary vs non-elementary result.

Newsgroups	comp.soft-sys.math.maple
Date	2015-05-06 09:52 -0700
Message-ID	<d00f3a7a-0ed5-498b-b3b7-e3f922c68da0@googlegroups.com> (permalink)
Subject	Elementary vs non-elementary result.
From	RGVickson@shaw.ca

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The following integration occurred in Physics Forums: 
int(f,x), where f = (x^2+1)/[(x^2-1)*sqrt(1+x^4)]. 

If asked for the indefinite integral int(f,x), Maple 11 (and Maple 14) return a nasty formula involving Elliptic functions. However, if asked for the definite integral int(f,x=0..z) assuming z>0, both versions of Maple return an explicit, closed-form function F(z)involving only elementary functions. Furthermore, dF/dz really does equal f(z)! (Initially, F(z) is complex because it involves an arctanh of an argument > 1, but an evalc on it yields a purely real expression defined for all z =/= 1, and again, which has the correct derivative.)

I just wonder why Maple was able to find an elementary expression for the  definite integral (but at any variable upper limit) but not for the indefinite integral.

RGV

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Elementary vs non-elementary result. RGVickson@shaw.ca - 2015-05-06 09:52 -0700
  Re: Elementary vs non-elementary result. "Nasser M. Abbasi" <nma@12000.org> - 2015-05-06 15:41 -0500
    Re: Elementary vs non-elementary result. RGVickson@shaw.ca - 2015-05-06 16:09 -0700
      Re: Elementary vs non-elementary result. "Nasser M. Abbasi" <nma@12000.org> - 2015-05-07 01:50 -0500
        Re: Elementary vs non-elementary result. acer <maple@rogers.com> - 2015-05-08 10:28 -0700
          Re: Elementary vs non-elementary result. "G. A. Edgar" <edgar@math.ohio-state.edu.invalid> - 2015-05-09 07:44 -0600
            Re: Elementary vs non-elementary result. acer <maple@rogers.com> - 2015-05-11 20:16 -0700
  Re: Elementary vs non-elementary result. acer <maple@rogers.com> - 2015-05-08 09:59 -0700
    Re: Elementary vs non-elementary result. RGVickson@shaw.ca - 2015-05-08 15:03 -0700

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