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MathGroup Archive 2006

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Re: Why does this lead to an answer with complex numbers?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg71459] Re: Why does this lead to an answer with complex numbers?
  • From: Peter Pein <petsie at dordos.net>
  • Date: Mon, 20 Nov 2006 02:43:36 -0500 (EST)
  • Organization: 1&1 Internet AG
  • References: <ejosmm$n3k$1@smc.vnet.net>

aaronfude at gmail.com schrieb:
> The expression is
> 
> \!\(FullSimplify[
>     Assuming[\[Beta] > 0 && \[Beta] < Pi/2,
>       Integrate[\(-Log[\@\(1 + x\^2\) - 1/11*x\ ]\), \ x]]]\)
> 
> Thanks!
> 
> Aaron Fude.
> 
Hi Aaron,

try a definite integral instead:

Assuming[Sqrt[1 + z^2] > z/11, FullSimplify[PiecewiseExpand[
    Integrate[-Log[Sqrt[1 + x^2] - (1/11)*x], {x, 0, z}]]]]

z + (1/(2*Sqrt[30]))*(11*(ArcTan[2*Sqrt[30]] - ArcTan[(2*Sqrt[30]*z)/11] -
     ArcTan[2*Sqrt[30]*Sqrt[1 + z^2]])) - z*Log[-(z/11) + Sqrt[1 + z^2]]


(PiecewiseExpand simplifies the If[z>0,...,Integrate[...]])

Peter


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