Services & Resources / Wolfram Forums / MathGroup Archive
-----

MathGroup Archive 2008

[Date Index] [Thread Index] [Author Index]

Search the Archive

Integrating x^b*Log[x]^m gives wrong result?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg85434] Integrating x^b*Log[x]^m gives wrong result?
  • From: KvS <keesvanschaik at gmail.com>
  • Date: Sun, 10 Feb 2008 05:19:51 -0500 (EST)

Dear all,

I'm running into the following problems with symbolic vs. numerical
integration of the function x^(-3.5)*Log[x]^m:

In[564]:=
ClearAll["Global`*"];
f1[m_]:=N[Integrate[x^(-3.5)*Log[x]^m,{x,5,10}]];
f2[m_]:=NIntegrate[x^(-3.5)*Log[x]^m,{x,5,10}];
Map[f1,{5,10,25,40}]
Map[f2,{5,10,25,40}]

Out[567]= {0.145434,4.62609,401145.,-9.30763*10^23}
Out[568]= {0.145434,4.62609,403156.,6.33616*10^10}

Of course the symbolic integration is wrong here since it shouldn't
yield a negative number. If the recursive formula resulting from
partial integration is used, things seem to go wrong as well:

In[572]:=
f[m_]:=(-1/2.5)*(10^(-2.5)*Log[10]^m-5^(-2.5)*Log[5]^m)+(m/
2.5)*f[m-1];
f[0]=(-1/2.5)*(10^(-2.5)-5^(-2.5));
Map[f,{5,10,25,40}]

Out[574]= {0.145434,4.62609,403156.,-2.54037*10^16}

So the result for m=25 still coincides with the one from NIntegrate,
while Integrate already gives something different; for m=40 the result
is different from both NIntegrate and Integrate (and wrong as it is
negative). If one changes the negative power of x to a positive one,
things seem ok btw.

Any clues what might be going on here?

Thanks in advance, Kees

In[533]:= $Version
Out[533]= 6.0 for Microsoft Windows (32-bit) (April 27, 2007)


  • Prev by Date: Re: IMS and Help Index
  • Next by Date: Re: How should I start with mathematica?
  • Previous by thread: Re: Import pdf problem
  • Next by thread: Re: Integrating x^b*Log ^m gives wrong result?