integrate issue (5.2)

*To*: mathgroup at smc.vnet.net*Subject*: [mg77081] integrate issue (5.2)*From*: dimitris <dimmechan at yahoo.com>*Date*: Sun, 3 Jun 2007 06:05:58 -0400 (EDT)

This is quite trivial so I am sure it has been pointed out a long time ago. In fact I believe that mathematica 6 does not show this buggy behavior. Anyway... In[32]:= $Version Out[32]= "5.2 for Microsoft Windows (June 20, 2005)" In[40]:= LaplaceTransform[Log[t], t, o] Out[40]= -((EulerGamma + Log[o])/o) which is correct. However In[42]:= Integrate[Log[t]*Exp[(-s)*t], {t, 0, Infinity}, GenerateConditions -> True] returns divergence message which is not in general truth. Try for example In[44]:= Integrate[(Log[t]*Exp[(-#1)*t] & ) /@ {1, 4, 10}, {t, 0, Infinity}] Out[44]= {-EulerGamma, -(EulerGamma/4) - Log[2]/2, (1/10)*(-EulerGamma - Log[10])} Being more specifying, In[47]:= Integrate[Log[t]*Exp[(-s)*t], {t, 0, Infinity}, Assumptions -> s > 0] Out[47]= -((EulerGamma + Log[s])/s) The integral converges for Re[s]>0, but Mathematica (5.2) fails to detect this.