simple timing question

*To*: mathgroup at smc.vnet.net*Subject*: [mg69920] simple timing question*From*: dimmechan at yahoo.com*Date*: Wed, 27 Sep 2006 06:05:25 -0400 (EDT)

Hi. Consider the following user defined function to calculate integrals with possible singulaties at the end points improperIntegrate[f_, x_, a_, b_] := With[{integral = Integrate[f, x]}, Limit[integral, x -> b, Direction -> 1] - Limit[integral, x -> a, Direction -> -1]] Then Timing[improperIntegrate[1/(2*x - 1)^(2/3), x, 1/2, 3]] {0.07800000000000001*Second, (3*5^(1/3))/2} Using directly Integrate almost 5 times more time is neeeded. Timing[Integrate[1/(2*x - 1)^(2/3), {x, 1/2, 3}]] {0.406*Second, (3*5^(1/3))/2} For me it sounds normally that Integrate needed more time. However I am looking for a clear explanation if possible. I believe it has to do that using directly Integrate much time is spent for checking for singularities (here 1/2). Am I right or/and there is another reason? Thanks in advance.

**Follow-Ups**:**Re: simple timing question***From:*Daniel Lichtblau <danl@wolfram.com>