diff --git a/src/methods/rule_based/rules2/8 Special functions/8.1 Bessel functions.jl b/src/methods/rule_based/rules2/8 Special functions/8.1 Bessel functions.jl
index 7072ddf..34c3fa5 100644
--- a/src/methods/rule_based/rules2/8 Special functions/8.1 Bessel functions.jl	
+++ b/src/methods/rule_based/rules2/8 Special functions/8.1 Bessel functions.jl	
@@ -1,6 +1,13 @@
 file_rules = [
     #(* ::Subsection::Closed:: *)
     #(* 8.1 Bessel functions *)
+    ("8_1_0",
+    :(*(~~a)) => :(
+    let
+        terms = distribute_special_function_product(arguments(~a), ~x)
+        terms === nothing ? nothing : sum(map(term -> ∫(term, ~x), terms))
+    end
+    ))
 
     (
         "8_1_1",
diff --git a/src/methods/rule_based/rules2/9 Miscellaneous/0.1 Integrand simplification rules.jl b/src/methods/rule_based/rules2/9 Miscellaneous/0.1 Integrand simplification rules.jl
index 98c5279..49ba6c7 100644
--- a/src/methods/rule_based/rules2/9 Miscellaneous/0.1 Integrand simplification rules.jl	
+++ b/src/methods/rule_based/rules2/9 Miscellaneous/0.1 Integrand simplification rules.jl	
@@ -1,14 +1,7 @@
 file_rules = [
+# 0_1_0: integral of the sum is sum of the integrals
 ("0_1_0", :(+(~~a)) => :(sum(map(f -> ∫(f,~x), arguments(~a)))) )
 
-("0_1_1",
-:(*(~~a)) => :(
-let
-    terms = distribute_special_function_product(arguments(~a), ~x)
-    terms === nothing ? nothing : sum(map(term -> ∫(term, ~x), terms))
-end
-))
-
 ("0_1_6",
 :((~!u)*((~!a)*(~v) + (~!b)*(~v) + (~!w))^(~!p)) => :(
     !contains_var((~a), (~b), (~x)) &&
@@ -28,6 +21,7 @@ end
     !contains_var((~a), (~x)) ?
 (~a)*(~x) : nothing))
 
+# constants out of the integral
 ("0_1_12",
 :(*(~~a)) => :(
 let
diff --git a/test/methods/rule_based/test_rule2.jl b/test/methods/rule_based/test_rule2.jl
index cbab46e..5231213 100644
--- a/test/methods/rule_based/test_rule2.jl
+++ b/test/methods/rule_based/test_rule2.jl
@@ -47,7 +47,8 @@ end
     @test eq(SymbolicIntegration.rule2(r, 1/exp(x)), -x)
 end
 
-@testset "special functions in rules" begin
+# This testset is for functions that are shorthand notation for powers, like exp and sqrt
+@testset "power shorthand functions in rules" begin
     @syms x
     rs = :(sqrt(~x)) => :(~x)
     @test eq(SymbolicIntegration.rule2(rs, sqrt(x)), x)
@@ -55,19 +56,6 @@ end
     rs = :(exp(~x)) => :(~x)
     @test eq(SymbolicIntegration.rule2(rs, exp(x+1)), x+1)
     @test eq(SymbolicIntegration.rule2(rs, ℯ^x), x)
-
-    rbj = :(besselj(~nu, ~z)) => :(~nu, ~z)
-    besselj_match = SymbolicUtils.arguments(SymbolicIntegration.rule2(rbj, SpecialFunctions.besselj(0, x)))
-    @test SymbolicUtils.unwrap_const(besselj_match[1]) == 0
-    @test isequal(besselj_match[2], x)
-
-    rbi = :(besseli(~nu, ~z)) => :(~nu, ~z)
-    besseli_match = SymbolicUtils.arguments(SymbolicIntegration.rule2(rbi, SpecialFunctions.besseli(1, x)))
-    @test SymbolicUtils.unwrap_const(besseli_match[1]) == 1
-    @test isequal(besseli_match[2], x)
-
-    rai = :(airyai(~z)) => :(~z)
-    @test eq(SymbolicIntegration.rule2(rai, SpecialFunctions.airyai(x)), x)
 end
 
 @testset "Segment" begin
diff --git a/test/methods/rule_based/test_special_functions.jl b/test/methods/rule_based/test_special_functions.jl
index 6788fb6..3fa5229 100644
--- a/test/methods/rule_based/test_special_functions.jl
+++ b/test/methods/rule_based/test_special_functions.jl
@@ -3,6 +3,9 @@ using SymbolicIntegration
 using SpecialFunctions
 using Symbolics
 
+# TODO move these tests to rundifficulttests.jl together with all the other integrals
+# putting all the integrals in a test files with the solutions
+
 @testset "RuleBased special-function integrals" begin
     @variables x a
     method = RuleBasedMethod()