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As mentioned in the comments these are related posts/answers: "NIntegrate over a list of functions", "How to avoid repetitive calculation when doing numerical integral?".

For more details how rules like ArrayOfFunctionsRule are implemented see "How to implement custom integration rules for use by NIntegrate?".

As mentioned in the comments these are related posts/answers: "NIntegrate over a list of functions", "How to avoid repetitive calculation when doing numerical integral?".

For more details how rules like ArrayOfFunctionsRule are implemented see "How to implement custom integration rules for use by NIntegrate?".

Convert the integrand matrix into a matrix of functions:

I1exprFS = 
  Map[Function[{fx}, Function[Evaluate[fx /. x -> #]]], I1expr, {2}];

Call NIntegrate with the new rule:

res1 =
    NIntegrate[1, {x, 0, 1}, 
      Method -> {"GlobalAdaptive", "SingularityHandler" -> None, 
        Method -> {ArrayOfFunctionsRule, "Functions" -> I1exprFS}}]; // AbsoluteTiming

(* {0.021779, Null} *)

Converting to functions:

funcs = 
  Map[Function[{fx}, Function[Evaluate[fx /. x -> #]]], 
   funcsExpr, {2}];

This integration is ~ 100 times faster than the default options one:

res1 = NIntegrate[1, {x, 0, 1}, 
   Method -> {"GlobalAdaptive", "SingularityHandler" -> None, 
     Method -> {ArrayOfFunctionsRule, 
       "Functions" -> funcs}}]; // AbsoluteTiming

(* {5.4292, Null} *)

Call NIntegrate with the new rule:

res1 =
    NIntegrate[1, {x, 0, 1}, 
      Method -> {"GlobalAdaptive", "SingularityHandler" -> None, 
        Method -> {ArrayOfFunctionsRule, "Functions" -> I1expr}}]; // AbsoluteTiming

(* {0.021779, Null} *)

This integration is ~ 100 times faster than the default options one:

res1 = NIntegrate[1, {x, 0, 1}, 
   Method -> {"GlobalAdaptive", "SingularityHandler" -> None, 
     Method -> {ArrayOfFunctionsRule, 
       "Functions" -> funcsExpr}}]; // AbsoluteTiming

(* {5.4292, Null} *)

Load the code for integration rule ArrayOfFunctionsRule:

Convert the integrand matrix into matrices of functions:

Load the code for the integration rule ArrayOfFunctionsRule:

Convert the integrand matrix into a matrix of functions: