In[]:=
ClearSystemCache[];prec=1000;g[x_]:=N[Log[x]/x,prec];Timing[MKB--(INIntegrate[Exp[-Pit+g[1+tI]],{t,0,Infinity},WorkingPrecisionprec,​​Method"Trapezoidal"]+N[I/Pi,prec])]
NIntegrate
:NIntegrate failed to converge to prescribed accuracy after 9 iterated refinements in t in the region {{0,∞}}. NIntegrate obtained 1008+1009 and 1013 for the integral and error estimates.
Out[]=
{0.5625,0.×
-1001
10
+0.×
-1001
10
}
In[]:=
ClearSystemCache[];prec=2000;g[x_]:=N[Log[x]/x,prec];Timing[MKB--(INIntegrate[Exp[-Pit+g[1+tI]],{t,0,Infinity},WorkingPrecisionprec,​​Method"Trapezoidal",MaxRecursion10])+1/PiI]
NIntegrate
:NIntegrate failed to converge to prescribed accuracy after 10 iterated refinements in t in the region {{0,∞}}. NIntegrate obtained 2008+2009 and 2014 for the integral and error estimates.
Out[]=
{4.54688,0.×
-2001
10
+0.×
-2001
10
}
In[]:=
ClearSystemCache[];prec=3000;g[x_]:=N[Log[x]/x,prec];Timing[MKB--(INIntegrate[Exp[-Pit+g[1+tI]],{t,0,Infinity},WorkingPrecisionprec,​​Method"Trapezoidal",MaxRecursion11]+1/PiI)]
NIntegrate
:NIntegrate failed to converge to prescribed accuracy after 11 iterated refinements in t in the region {{0,∞}}. NIntegrate obtained 3008+3009 and 3014 for the integral and error estimates.
Out[]=
{18.125,0.×
-3001
10
+0.×
-3001
10
}
In[]:=
ClearSystemCache[];prec=4000;g[x_]:=N[Log[x]/x,prec];Timing[MKB--(INIntegrate[Exp[-Pit+g[1+tI]],{t,0,Infinity},WorkingPrecisionprec,​​Method"Trapezoidal",MaxRecursion11]+1/PiI)]
NIntegrate
:NIntegrate failed to converge to prescribed accuracy after 11 iterated refinements in t in the region {{0,∞}}. NIntegrate obtained 4008+4009 and 4014 for the integral and error estimates.
Out[]=
{42.6875,0.×
-4001
10
+0.×
-4001
10
}
In[]:=
ClearSystemCache[];prec=5000;g[x_]:=N[Log[x]/x,prec];Timing[MKB--(INIntegrate[Exp[-Pit+g[1+tI]],{t,0,Infinity},WorkingPrecisionprec,​​Method"Trapezoidal",MaxRecursion12]+I/Pi)]
NIntegrate
:NIntegrate failed to converge to prescribed accuracy after 12 iterated refinements in t in the region {{0,∞}}. NIntegrate obtained 5008+5009 and 5014 for the integral and error estimates.
{138.171875`,0``5000.579416043584+0``5000.579416043584}
In[]:=
m+MKB
Out[]=
0.×
-5001
10
+0.×
-5001
10

In[]:=
ClearSystemCache[];prec=10000;g[x_]:=N[Log[x]/x,prec];Timing[MKB+(INIntegrate[Exp[-Pit+g[1+tI]],{t,0,Infinity},WorkingPrecisionprec,​​Method"Trapezoidal",MaxRecursion13]+I/Pi)]
NIntegrate
:NIntegrate failed to converge to prescribed accuracy after 13 iterated refinements in t in the region {{0,∞}}. NIntegrate obtained 10009+10010 and 10015 for the integral and error estimates.
Out[]=
{1468.44,0.×
-10001
10
+0.×
-10001
10
}
In[]:=
ClearSystemCache[];prec=20000;g[x_]:=N[Log[x]/x,prec];Timing[MKB--(INIntegrate[Exp[-Pit+g[1+tI]],{t,0,Infinity},WorkingPrecisionprec,​​Method"Trapezoidal",MaxRecursion14]+I/Pi)]
NIntegrate
:NIntegrate failed to converge to prescribed accuracy after 14 iterated refinements in t in the region {{0,∞}}. NIntegrate obtained 20009+20010 and 20016 for the integral and error estimates.
Out[]=
{9486.41,0.×
-20001
10
+0.×
-20001
10
}
In[]:=
ClearSystemCache[];prec=40000;g[x_]:=N[Log[x]/x,prec];Timing[MKB--(INIntegrate[Exp[-Pit+g[1+tI]],{t,0,Infinity},WorkingPrecisionprec,Method"Trapezoidal",MaxRecursion15]+I/Pi)]
NIntegrate
:NIntegrate failed to converge to prescribed accuracy after 15 iterated refinements in t in the region {{0,∞}}. NIntegrate obtained 40009+40010 and 40016 for the integral and error estimates.
Out[]=
{73961.4,0.×
-40001
10
+0.×
-40001
10
}