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Re: [Integrate] Why two results of same eq. are different?

• To: mathgroup at smc.vnet.net
• Subject: [mg44706] Re: [mg44655] [Integrate] Why two results of same eq. are different?
• From: Vladimir Bondarenko <vvb at mail.strace.net>
• Date: Fri, 21 Nov 2003 05:13:27 -0500 (EST)
• References: <200311200816.DAA01508@smc.vnet.net>
• Reply-to: Vladimir Bondarenko <vvb at mail.strace.net>
• Sender: owner-wri-mathgroup at wolfram.com

SJK> I got very extraordinary results today from below two same integrals
SJK> except one is symbolic one and the other is numeric one:
SJK> A. In[1]= N[Integrate[ Log[2, 1 + 10*x]*Exp[-x]*x, {x, 0, Infinity}]]
SJK>     Out[1]= -3.77002
SJK> B. In[2]= NIntegrate[ Log[2, 1 + 10*x]*Exp[-x]*x, {x, 0, Infinity}]
SJK>     Out[2]= 4.05856

SJK> Why did I got the different results of these, surprisingly?

This is a so-called regression bug (the current version cannot do
what the previous one did correctly).

This bug was introduced in Mathematica 4.0 (April 21, 1999).

Mathematica 3.0 (April 25, 1997) returns a valid value for your
integral producing  (9*I*E^(1/10)*Pi)/(10*Log[2]) - (-10 + 9*E^\
(1/10)*(I*Pi + ExpIntegralEi[-(1/10)]))/(10*Log[2]) which is just

   1/10*(9*Exp[1/10]*ExpIntegralE[1, 1/10] + 10)/Log[2] //N

   4.05856


Cheers,

Vladimir Bondarenko

http://www.cybertester.com/

• References:
  • [Integrate] Why two results of same eq. are different?
    • From: "Sung Jin Kim" <kimsj@mobile.snu.ac.kr>