(∫_0^1) (x^20) Exp[x]dx

$Version

Integrand

fi = x^20  Exp[x]

Numerische Integration

an = NIntegrate[fi,{x,0,1}]

Analytische Integration

ai = Integrate[fi,{x,0,1}]//Expand

Resultate

N[ai]

ain = N[ai,20]

N[an,20]

Resultat der analytischen Integration numerisch ausgewertet

ai[[1]]

ai[[2,1]]

N[E,30]

t1 = %  %%

t2 = N[ai[[1]],30]

% + %%

integration ueber die Reihenentwicklung des Integranden

se = Series[fi,{x,0,30}]

Integrate[Normal[se],{x,0,1}]

sen = N[%]

an == ain

sen == ain

sen - ain

testdiff[vv1_,vv2_]= If[Abs[vv1 - vv2]< 10^-9.,True,False];

testdiff[sen, ain]