Assuming[e>0,Integrate[Sqrt[u]/(e+u),{u,0,Infinity}]](*Acorrectanswer*)
Integrate
:Integral of
u
e+u
does not converge on {0,∞}.
Out[]=
∞
∫
0
u
e+u
u
In[]:=
Assuming[e>0,Integrate[Sqrt[u]/(e+u),{u,0,Infinity},GenerateConditions->False]](*ProbablyusessomeRegularizationfornotconvergeintegrals!*)
Out[]=
-
e
π
(*Using:*)
In[]:=
Limit[u^-s,s->0](*OK*)
Out[]=
1
(*Then:*)
In[]:=
Assuming[{e>0,s>0},Integrate[Sqrt[u]/(e+u)*u^-s,{u,0,Infinity}]]
Out[]=
-
1
2
-s
e
πSec[πs] if
1
2
<s<
3
2
In[]:=
Limit[%[[1]],s->0]
Out[]=
-
e
π