Вычисление несобственных интегралов

Clear["Global`*"]
f=1/(1+x^2);
Integrate[f,{x,-Infinity,Infinity}]
Plot[f,{x,-10,10}]

Clear["Global`*"]

f=1/Sqrt[1-x^2];
Integrate[f,{x,0,1}]
Plot[f,{x,-1,1},PlotRange->{0,2}]

Clear["Global`*"]

f=1/(x Log[x]^p);
Integrate[f,{x,Exp[1],Infinity},Assumptions->p∈Reals]

Plot[
Evaluate[1/(x Log[x]^#)&/@ {1,2,3}] ,{x,-0.5,2},
PlotStyle->{Null, Dashed,DotDashed},
PlotLegends->"Expressions",
Exclusions->1]