diff --git a/ext/QuadGKEnzymeExt.jl b/ext/QuadGKEnzymeExt.jl
index d10d21a..9d4c9b7 100644
--- a/ext/QuadGKEnzymeExt.jl
+++ b/ext/QuadGKEnzymeExt.jl
@@ -84,10 +84,37 @@ function Base.:*(a::ClosureVector, b::Number)
     return b*a
 end
 
-function Enzyme.EnzymeRules.reverse(config, ofunc::Const{typeof(quadgk)}, dres::Active, cache, f::Union{Const, Active}, segs::Annotation{T}...; kws...) where {T}
+struct MixedClosureVector{F}
+    f::Base.RefValue{F}
+end
+
+function Base.:+(a::CV, b::CV) where {CV <: MixedClosureVector}
+    res = deepcopy(a)::CV
+    Enzyme.Compiler.recursive_accumulate(res, b, identity)
+    res
+end
+
+function Base.:-(a::CV, b::CV) where {CV <: MixedClosureVector}
+    res = deepcopy(a)::CV
+    Enzyme.Compiler.recursive_accumulate(res, b, x->-x)
+    res
+end
+
+function Base.:*(a::Number, b::CV) where {CV <: MixedClosureVector}
+    # b + (a-1) * b = a * b
+    res = deepcopy(b)::CV
+    Enzyme.Compiler.recursive_accumulate(res, b, x->(a-1)*x)
+    res
+end
+
+function Base.:*(a::MixedClosureVector, b::Number)
+    return b*a
+end
+
+function Enzyme.EnzymeRules.reverse(config, ofunc::Const{typeof(quadgk)}, dres::Active, cache, f::Union{Const, Active, MixedDuplicated}, segs::Annotation{T}...; kws...) where {T}
     df = if f isa Const
         nothing
-    else
+    elseif f isa Active
         segbuf = cache[1]
         fwd, rev = Enzyme.autodiff_thunk(ReverseSplitNoPrimal, Const{typeof(call)}, Active, typeof(f), Const{T})
         _df, _ = quadgk(map(x->x.val, segs)...; kws..., eval_segbuf=segbuf, maxevals=0, norm=f->0) do x
@@ -96,6 +123,17 @@ function Enzyme.EnzymeRules.reverse(config, ofunc::Const{typeof(quadgk)}, dres::
             return ClosureVector(drev[1][1])
         end
         _df.f
+    elseif f isa MixedDuplicated
+        segbuf = cache[1]
+        fwd, rev = Enzyme.autodiff_thunk(ReverseSplitNoPrimal, Const{typeof(call)}, Active, typeof(f), Const{T})
+        _df, _ = quadgk(map(x->x.val, segs)...; kws..., eval_segbuf=segbuf, maxevals=0, norm=f->0) do x
+            fshadow = Ref(Enzyme.make_zero(f.val))
+            tape, prim, shad = fwd(Const(call), MixedDuplicated(f.val, fshadow), Const(x))
+            drev = rev(Const(call), f, Const(x), dres.val[1], tape)
+            return MixedClosureVector(fshadow)
+        end
+        Enzyme.Compiler.recursive_accumulate(f.dval, _df.f)
+        nothing
     end
     dsegs1 = segs[1] isa Const ? nothing : -LinearAlgebra.dot(f.val(segs[1].val), dres.val[1])
     dsegsn = segs[end] isa Const ? nothing : LinearAlgebra.dot(f.val(segs[end].val), dres.val[1])