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>