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Evaluate integral that involves derivatives?

Posted 4 months ago
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I have an analytical expression that I want to evaluate (please see the attached picture). Here is the code I tried `s[r_]=[Alpha] * r ;

xxSum[r_] := Sum[(-s[r])^kk/kk!*D[G[r], {r, kk}], {kk, 0, 4}];
xxLAB[r_] := xxSum[r]*f[r];
A = NIntegrate[xxLAB[r], {r, 100, Infinity}] `

The above code did not work. I appreciate your help

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 s[r_, \[Alpha]_] := \[Alpha]*r
 G[r_] := Exp[-r] (* I assume *)
 f[r_] := Sin[r]  (* I assume *)

 xxSum[r_, \[Alpha]_] := Sum[(-s[r, \[Alpha]])^k/k!*D[G[r], {r, k}], {k, 0, 4}];
 xxLAB[r_, \[Alpha]_] := xxSum[r, \[Alpha]]*f[r];
 A[\[Alpha]_] := NIntegrate[xxLAB[r, \[Alpha]], {r, 100, Infinity}]; 
 A[10^10] (* I assume  alpha = 10^10  *)
 (* 303.243 *)
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