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Re: Mathematica gives bad integral ??

• To: mathgroup at smc.vnet.net
• Subject: [mg24324] Re: Mathematica gives bad integral ??
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Sun, 9 Jul 2000 04:52:34 -0400 (EDT)
• Organization: Universitaet Leipzig
• References: <8k3n38$3pk@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

I don't know an explanation because

ires = FullSimplify[Integrate[1/Sqrt[1 - Sin[2x]], x]];


(ArcTanh[(1 + Tan[x/2])/Sqrt[2]]*(Cos[x] - Sin[x]))/
 Sqrt[1/2 - Cos[x]*Sin[x]]

and

D[ires, x] // FullSimplify 

gives

1/Sqrt[1 - Sin[2*x]]

Since you don't supply any Input I can only tell you
that Mathematica has no error.

Regards
  Jens

"J.R. Chaffer" wrote:
> 
> Hi,  this newbie gets erroneous results with Mathematica
> 4.0 (for students), with the following integral.  Hopefully
> someone can tell me why, and what I may be doing
> wrong.  I have tried "Assumptions -> x e Reals", or
> x > 0, with same results.  Integral in question is,
> 
> Integrate[1/Sqrt[1-Sin[2x]]]
> 
> The result is somewhat involved, instead of the expected
> result (Schaum, "Calculus" 4E, p. 297),
> 
>   integral = - (1/Sqrt[2])Log[Abs[Csc[Pi/4-x]-Cot[Pi/4-x]]]
> 
> One expects to get differing forms with any computer
> algebra system, since there are so many equivalent forms
> of algebraic expressions.  However, Mathematica's form
> and the Schaum (correct) form differ by significant
> numerical values, as plotting shows (i.e., not some E-16
> or some such).
> 
> Further, and what really seems wrong, is that when one
> differentiates Mathematica's result for the integral, one
> does NOT get the original integrand, or anything even
> close, numerically.
> 
> So, I am confused.  Anyone who knows the explanation
> would be welcome to share it.
> 
> Thank you.
> 
> John Chaffer