How to create and plot a function involving NIntegrate

I am interested in understanding the growth of the following function for $$n\geq 2$$ $$I(n) = \int_{0}^{1/2}\frac{ds}{s^{1-1/n}+(1-s)^{1-1/n}-1}.$$

I can explicitly compute $$I(n)$$ for various values of $$n$$ using NIntegrate

phi[n_, s_] = s^(1 - 1/n) + (1 - s)^(1 - 1/n) - 1;
NIntegrate[1/phi[2, s], {s, 0, 1/2}]


but I would like to plot this on a graph for integer values $$2\leq n\leq 100$$ however I am not sure how to do this in Mathematica. Any suggestions will be much appreciated.

• Do you mean something like: phi[n_, s_] := s^(1 - 1/n) + (1 - s)^(1 - 1/n) - 1; i[n_] := NIntegrate[1/phi[n, s], {s, 0, 1/2}]; ListPlot[Table[{n, i[n]}, {n, 2, 200}]]? Note, however, that there are precision issues for $n\geq 8$. Jul 25 at 12:50
• To avoid messages use phi[n_, s_] := s^(1 - 1/n) + (1 - s)^(1 - 1/n) - 1; i[n_] := NIntegrate[1/phi[n, s], {s, 0, 1/2}, PrecisionGoal -> 2, AccuracyGoal -> 5] Jul 25 at 15:55
• This gives an accurate table in 3.3 sec.: data = Table[NIntegrate[1/phi[n, s], {s, 0, 1/10, 1/2}, Method -> {"GlobalAdaptive", "SingularityHandler" -> {"IMT", "TuningParameters" -> 2}, "SingularityDepth" -> 2, "SymbolicProcessing" -> 0, Method -> {"GaussKronrodRule", "Points" -> 11}}, PrecisionGoal -> 6, WorkingPrecision -> 24], {n, 2, 200}]; Jul 25 at 23:47