In[]:=
g[x_]=x^(1/x);Timing[N[Quiet[M2=NIntegrate[Exp[IPit](g[t]-1),{t,1,InfinityI},WorkingPrecision1000,Method"Trapezoidal",MaxRecursion10]]]]
Out[]=
{6.45313,0.070776-0.0473806}
In[]:=
g[x_]=x^(1/x);Timing[N[Quiet[M2-NIntegrate[Exp[IPit](g[t]-1),{t,1,InfinityI},WorkingPrecision1000,Method"MultiPeriodic",MaxRecursion10]]]]
Out[]=
{2.375,1.70529×+1.11456×}
-24
10
-45
10
In[]:=
g[x_]=x^(1/x);Timing[N[Quiet[M2-NIntegrate[Exp[IPit](g[t]-1),{t,1,InfinityI},WorkingPrecision1000,Method"GlobalAdaptive",MaxRecursion10]]]]
-924
10
-924
10
Out[]=
{24.75,0.+0.}
In[]:=
g[x_]=x^(1/x);Timing[N[Quiet[M2-NIntegrate[Exp[IPit](g[t]-1),{t,1,InfinityI},WorkingPrecision1000,Method"LocalAdaptive",MaxRecursion10]]]]
Out[]=
$Aborted
In[]:=
g[x_]=x^(1/x);Timing[N[Quiet[M2-NIntegrate[Exp[IPit](g[t]-1),{t,1,InfinityI},WorkingPrecision1000,Method"DoubleExponential",MaxRecursion10]]]]
Out[]=
{6.60938,0.+0.}
(∞
∫
1
In[]:=
g[x_]=x^(1/x);Timing[N[Quiet[M2-NIntegrate[Exp[IPit](g[t]-1),{t,1,InfinityI},WorkingPrecision1000,Method"DoubleExponential",MaxRecursion10]]]]
Out[]=
{6.01563,0.+0.}
∞
∫
1
1
2
π
In[]:=
g[x_]=x^(1/x);Timing[N[Quiet[M2-(1/Pi^2+NIntegrate[Exp[IPit](g[t]-t),{t,1,InfinityI},WorkingPrecision100,Method"DoubleExponential",MaxRecursion10])],40]]
Out[]=
{0.046875,0.×+0.×}
-102
10
-102
10
∞
∫
1
2
t
2
2
π
2
3
π
In[]:=
g[x_]=x^(1/x);Timing[N[Quiet[M2-(2/Pi^2+2/Pi^3I+NIntegrate[Exp[IPit](g[t]-t^2),{t,1,InfinityI},WorkingPrecision100,Method"DoubleExponential",MaxRecursion10])],40]]
Out[]=
{0.046875,0.×+0.×}
-101
10
-101
10
In[]:=
g[x_]=x^(1/x);TimingNQuietM2--+6Pi^3I+NIntegrate[Exp[IPit](g[t]-t^3),{t,1,InfinityI},WorkingPrecision100,Method"DoubleExponential",MaxRecursion10],40
3
2
π
6
4
π
Out[]=
{0.046875,0.×+0.×}
-101
10
-101
10
In[]:=
N[(Timing[test=(NIntegrate[(Exp[Log[t]/t-Pit/I]),{t,1,InfinityI},WorkingPrecision4453,Method"Trapezoidal",MaxRecursion11]+I/Pi)])]
Out[]=
{157.938,0.070776-0.0473806}
200018300038Method(A,BorC)secdigitsABC20002320183000968036400016514164500044241838660006235915441000032503070200040000175,551164,005MethodA:g[x_]=x^(1/x);t=(Timing[test3=-(INIntegrate[(g[(1+tI)])/(Exp[Pit]),{t,0,Infinity},WorkingPrecision40000,Method"Trapezoidal",MaxRecursion15]+I/Pi)])[[1]];MethodB:Timing[NIntegrate[I(f[It]),{t,0,Infinity},WorkingPrecision40000,Method"Trapezoidal",MaxRecursion15]]MethodC:N[(Timing[(NIntegrate[(Exp[Log[t]/t-Pit/I]),{t,1,InfinityI},WorkingPrecision40000,Method"Trapezoidal",MaxRecursion15]+I/Pi)])]64000784,937=218hours,halfadaylongerthanthe35,000usingthelongcode.
In[]:=
g[x_]=x^(1/x);Timing[N[Quiet[M2=NIntegrate[Exp[IPit](g[t]-1),{t,1,InfinityI},WorkingPrecision6000,Method"Trapezoidal",MaxRecursion12]]]]
Out[]=
{596.609,0.070776-0.0473806}
In[]:=
N[(Timing[M2-(NIntegrate[(Exp[Log[t]/t-Pit/I]),{t,1,InfinityI},WorkingPrecision5000,Method"Trapezoidal",MaxRecursion12]+I/Pi)]),20]