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integrate issue (5.2)


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.



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