In[]:=
Timing[​​MKB-Quiet[NIntegrate[​​Exp[PiIx]Sum[(Log[x]/x)^n/n!,{n,1,Infinity}],{x,1,​​InfinityI},WorkingPrecision1000,Method"Trapezoidal"]]]
Out[]=
{1.8125,0.×
-1002
10
+0.×
-1002
10
}
In[]:=
Timing[​​MKB-Quiet[NIntegrate[​​Exp[PiIx]Sum[(Log[x]/x)^n/n!,{n,1,Infinity}],{x,1,​​InfinityI},WorkingPrecision2000,Method"Trapezoidal",​​MaxRecursion10]]]
Out[]=
{12.4844,0.×
-2002
10
+0.×
-2002
10
}
In[]:=
Timing[​​MKB-Quiet[NIntegrate[​​Exp[PiIx]Sum[(Log[x]/x)^n/n!,{n,1,Infinity}],{x,1,​​InfinityI},WorkingPrecision3000,Method"Trapezoidal",​​MaxRecursion11]]]
Out[]=
{53.4063,0.×
-3002
10
+0.×
-3002
10
}
In[]:=
Timing[​​MKB-Quiet[NIntegrate[​​Exp[PiIx]Sum[(Log[x]/x)^n/n!,{n,1,Infinity}],{x,1,​​InfinityI},WorkingPrecision4000,Method"Trapezoidal",​​MaxRecursion11]]]
Out[]=
{94.375,0.×
-4002
10
+0.×
-4002
10
}
In[]:=
Timing[​​MKB-Quiet[NIntegrate[​​Exp[PiIx]Sum[(Log[x]/x)^n/n!,{n,1,Infinity}],{x,1,​​InfinityI},WorkingPrecision5000,Method"Trapezoidal",​​MaxRecursion12]]]
Out[]=
{285.813,0.×
-5002
10
+0.×
-5002
10
}
In[]:=
ClearSystemCache[];Timing[​​MKB-Quiet[NIntegrate[​​Exp[PiIx]Sum[(Log[x]/x)^n/n!,{n,1,Infinity}],{x,1,​​InfinityI},WorkingPrecision10000,Method"Trapezoidal",​​MaxRecursion13]]]
Out[]=
{2204.64,0.×
-10002
10
+0.×
-10002
10
}
ClearSystemCache[];Timing[​​MKB-Quiet[NIntegrate[​​Exp[PiIx]Sum[(Log[x]/x)^n/n!,{n,1,Infinity}],{x,1,​​InfinityI},WorkingPrecision40000,Method"Trapezoidal",​​MaxRecursion15]]]
Out[]=
{114362.,0.×
-40002
10
+0.×
-40002
10
}
In[]:=
ClearSystemCache[];Timing[​​MKB-Quiet[NIntegrate[​​Exp[PiIx]Sum[(Log[x]/x)^n/n!,{n,1,Infinity}],{x,1,​​InfinityI},WorkingPrecision1000,Method"Trapezoidal"]]]
Out[]=
{2.04688,0.×
-1002
10
+0.×
-1002
10
}