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5.2 vs 4.0

• To: mathgroup at smc.vnet.net
• Subject: [mg73237] 5.2 vs 4.0
• From: "dimitris" <dimmechan at yahoo.com>
• Date: Thu, 8 Feb 2007 03:42:23 -0500 (EST)

I know that definite integration convergence tests in versions 5.X try
"harder" and this fact may cause some definite integrals to be
evaluated in more time than in previous version but even in view of
this fact I can't understand the following difference in the time-
performances of 5.2 and 4.0 in the following definite integral

(*version 5.2*)
Timing[Integrate[x^2*Sin[x]^4*Cos[x]^3*Log[x], {x, 0, Pi}]]
{217.18800000000002*
    Second, -((152*Pi*(1 + 2*Log[Pi]))/3675) + (3*SinIntegral[Pi])/
      32 - (1/288)*SinIntegral[3*Pi] - SinIntegral[5*Pi]/4000 +
    SinIntegral[7*Pi]/10976}

N[%[[2]]]
-0.2598830637647862

(*version 4.0*)
Timing[Integrate[x^2*Sin[x]^4*Cos[x]^3*Log[x], {x, 0, Pi}]]
{2.141*Second, (-510720*Pi - 1021440*Pi*Log[Pi] +
1157625*SinIntegral[Pi] -
        42875*SinIntegral[3*Pi] - 3087*SinIntegral[5*Pi] +
        1125*SinIntegral[7*Pi])/12348000}

N[%[[2]]]
-0.2598830637647862

(*numerical check, both 5.2 and 4.0*)
NIntegrate[x^2*Sin[x]^4*Cos[x]^3*Log[x], {x, 0, Pi}]
-0.25988306376497605

Any ideas/comments?

Dimitris