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"]+I/Pi)]
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[]=
{5.75399,(-0.0707760393115288035395280218302820013657546962033630275831727881636184572643820365808318812661772382094407339691097179269990446453847536429225844386065219333047122290612020548398576433662343489843827071049989705395231226917848529903218507274354522005125732810542217424931317767029586377171448965877929118571617511540562365603991484881752820025072306153573457106503145899219683164868123907954938255650974196758814736254874320591902869577457241143992751659339102999273310798274679484513088932825130726310257008303152743086102342833436910409821702262269045940297055093272952022662549075225941956559080574835998923469310063614655255062971317960148313404503841687805492907298185104582941328637784284366753787303942475197280648872877809986710218877979777725224197655941725692774900310719381777491848349627938468198411955193898347075098152638657614980900350262780319142430252921925131515239611841070722530473939496294305264627977744876814858325335947117076721493110160508928494597906728688873533031986215124+0.6840003894379321291827444599926611267109914826549994343226303771381530581249766381509598342127214786722379645160914886099586780498831455794087390519118879988351918366211827085883779918191195794251385436100844782462528597869421390620796113023053439642582325892202911183326091512210367124716901047132601108752764946385830438156754378694878046808312868541961166205744280461776232345922905313658259576212809654022016030244583148587352474339130505540080799774619683572540292971258866450201101870835703060314349396491402064932644813564545345219868887520119503538181776359577265099302389566135475579468144849763261779452665955246258699867927165904920865474653323437547890996263309008000635821390872899085050267595499289350292064426374257860050360480985983040929967531455890126454745336170703768670865452282230609404349352192528853332983902723422349528708833041166404094214527652846093649412053441225697816347825083686411267665287070199573408950619362466450657531019167812545570069898184092833171458371673460)+MKB}
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][[1]]
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[]=
34.944
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)][[1]]
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[]=
140.425
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[]=
{76.5938,0.×
-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.
Out[]=
{230.703,0.×
-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[]=
{1754.63,0.×
-10001
10
+0.×
-10001
10
}
In[]:=
Pause[100]
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[]=
{12620.6,0.×
-20001
10
+0.×
-20001
10
}
In[]:=
MaxMemoryUsed[]
Out[]=
203130136
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[]=
{90983.2,0.×
-40001
10
+0.×
-40001
10
}