(*  Calculate a natural logarithm using Simpson's Rule  *)
(*  \(Integral)ab​ f(x) dx \(TildeTilde) (b-a)/(3n)(FIRST+4(sum of ODDs) +2(sum of EVENs)+LAST)  *)

aTobStrip = 1000;

a = 1;
b = 2;  (*  log(b)  *)

funDom = Table(n, {n, a*aTobStrip, b*aTobStrip});
listSize = Length(funDom);

evenIndex = Select(Table(n, {n, 1, listSize}), EvenQ);
oddIndex = Select(Table(n, {n, 2, listSize - 1}), OddQ);

f(x_) := 1/x;

funRan = Replace(funDom, {n_ -> N(f(n/aTobStrip), 14)});

firstItem = funRan[[1]];
lastItem = funRan[[listSize]];

evenItems =funRan[[evenIndex]]*4;
oddItems = funRan[[oddIndex]]*2;

rangeSum = firstItem + Total(Join(evenItems, oddItems)) + lastItem;

answer = (b-a) / 3 / aTobStrip * rangeSum;

N(answer, 14)