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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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