Integral not linear for discontinuous integrand in QuadGKL

[marvel-markus]

Describe the bug 🐞

Integrating a function using QuadGKL is sometimes not linear in the function.

Expected behavior

The integral of a function is linear in the function. Hence first multiplying by a constant and then integrating or vice versa should yield the same result.

Minimal Reproducible Example 👇

using Integrals

n=100.0
en=1.0e-6
g=(x->x*( ((x<en) ? 1/sqrt(en-x+1.0e-8) : 0.)))

println(n*(solve(IntegralProblem((x,p)-> g(x), (0.0,2*en)), QuadGKJL()).u))
#returns 
#6.735787033968866e-8
println(solve(IntegralProblem((x,p)-> n*g(x), (0.0,2*en)), QuadGKJL()).u)
#returns 
#1.1520675757937744e-7
println("exact result: $((-151 + 101*sqrt(101))/7500000000)")
#returns 
#1.1520499169776132e-7

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

Status `~/.julia/environments/v1.12/Project.toml`
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Info Packages marked with ⌃ have new versions available and may be upgradable.

• Output of using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)

Status `~/.julia/environments/v1.12/Manifest.toml`
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  [1a1011a3] SharedArrays v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.12.0
  [f489334b] StyledStrings v1.11.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test v1.11.0
  [cf7118a7] UUIDs v1.11.0
  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.3.0+1
  [781609d7] GMP_jll v6.3.0+2
  [deac9b47] LibCURL_jll v8.15.0+0
  [e37daf67] LibGit2_jll v1.9.0+0
  [29816b5a] LibSSH2_jll v1.11.3+1
  [3a97d323] MPFR_jll v4.2.2+0
  [14a3606d] MozillaCACerts_jll v2025.11.4
  [4536629a] OpenBLAS_jll v0.3.29+0
  [05823500] OpenLibm_jll v0.8.7+0
  [458c3c95] OpenSSL_jll v3.5.4+0
  [efcefdf7] PCRE2_jll v10.44.0+1
  [bea87d4a] SuiteSparse_jll v7.8.3+2
  [83775a58] Zlib_jll v1.3.1+2
  [8e850b90] libblastrampoline_jll v5.15.0+0
  [8e850ede] nghttp2_jll v1.64.0+1
  [3f19e933] p7zip_jll v17.7.0+0
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`

• Output of versioninfo()

Julia Version 1.12.4
Commit 01a2eadb047 (2026-01-06 16:56 UTC)
Build Info:
  Official https://julialang.org release
Platform Info:
  OS: macOS (arm64-apple-darwin24.0.0)
  CPU: 10 × Apple M1 Pro
  WORD_SIZE: 64
  LLVM: libLLVM-18.1.7 (ORCJIT, apple-m1)
  GC: Built with stock GC
Threads: 1 default, 1 interactive, 1 GC (on 8 virtual cores)

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