# \#integral

**URL:** https://discourse.julialang.org/tag/integral/576.md

[Latest](https://discourse.julialang.org/latest.md) · [Categories](https://discourse.julialang.org/categories.md) · [Tags](https://discourse.julialang.org/tags.md)

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## [\[ANN\] HAdaptiveIntegration.jl v1.0.0 - Adaptive numerical integration over simplices and orthotopes](https://discourse.julialang.org/t/ann-hadaptiveintegration-jl-v1-0-0-adaptive-numerical-integration-over-simplices-and-orthotopes/135309)

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**Author:** [@zmoitier](https://discourse.julialang.org/u/zmoitier)\
**Replies:** 1\
**Last updated:** [April 6, 2026, 9:10am UTC](https://discourse.julialang.org/t/ann-hadaptiveintegration-jl-v1-0-0-adaptive-numerical-integration-over-simplices-and-orthotopes/135309 "2026-04-06T09:10:39Z")

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The HAdaptiveIntegration.jl package is designed for numerical integration over multidimensional domains. It computes integrals of the form I = \\int\_{\\Omega} f(x) \\, \\mathrm{d}x where f is any Julia function and \\Omega re…

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## [Caching in Integrals.jl](https://discourse.julialang.org/t/caching-in-integrals-jl/135443)

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**Author:** [@omerc](https://discourse.julialang.org/u/omerc)\
**Replies:** 4\
**Last updated:** [February 5, 2026, 2:25am UTC](https://discourse.julialang.org/t/caching-in-integrals-jl/135443 "2026-02-05T02:25:25Z")

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Recently, I tried to numerically integrate a function for multiple parameters. The integral is four dimensional, so I use CubatureJLh() (but I don’t mind using other methods - the documentation doesn’t elaborate a lot on…

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## [Tanh-Sinh Quadrature package](https://discourse.julialang.org/t/tanh-sinh-quadrature-package/135114)

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**Author:** [@svretina](https://discourse.julialang.org/u/svretina)\
**Replies:** 4\
**Last updated:** [January 17, 2026, 11:50pm UTC](https://discourse.julialang.org/t/tanh-sinh-quadrature-package/135114 "2026-01-17T23:50:08Z")

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Hi everyone, before I tag an official release and make an official announcement for this package (GitHub - svretina/FastTanhSinhQuadrature.jl: A Julia package for Tanh-Sinh Quadrature rules up to 3 dimensions). I would …

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## [\[ANN\] SymbolicIntegration.jl - indefinite integration with Symbolics.jl symbols](https://discourse.julialang.org/t/ann-symbolicintegration-jl-indefinite-integration-with-symbolics-jl-symbols/134777)

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**Author:** [@CiccioPasticcio](https://discourse.julialang.org/u/CiccioPasticcio)\
**Replies:** 28\
**Last updated:** [January 5, 2026, 10:12am UTC](https://discourse.julialang.org/t/ann-symbolicintegration-jl-indefinite-integration-with-symbolics-jl-symbols/134777 "2026-01-05T10:12:25Z")

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For a while now I have been developing SymbolicIntegration.jl, that lets you solve symbolic integrals in julia! it has for now two different methods to arrive at the antiderivative: Risch algorithm Rule based method us…

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## [Speeding up N-dimensional integration](https://discourse.julialang.org/t/speeding-up-n-dimensional-integration/132782)

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**Author:** [@owiecc](https://discourse.julialang.org/u/owiecc)\
**Replies:** 14\
**Last updated:** [October 1, 2025, 2:17pm UTC](https://discourse.julialang.org/t/speeding-up-n-dimensional-integration/132782 "2025-10-01T14:17:14Z")

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I am struggling to speed up a N-dimensional integration problem. To me it looks that allocations are the problem. I chased as many allocations I could find in the code but I still would like to speed-up the code by at le…

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## [Common API for \`Integrate\`. IntegrationBase](https://discourse.julialang.org/t/common-api-for-integrate-integrationbase/130637)

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**Author:** [@misha\_mikhasenko](https://discourse.julialang.org/u/misha_mikhasenko)\
**Replies:** 5\
**Last updated:** [July 11, 2025, 6:30pm UTC](https://discourse.julialang.org/t/common-api-for-integrate-integrationbase/130637 "2025-07-11T18:30:02Z")

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I’ve observed a conflict of different packages exporting integrate (e.g.). It would be nice to have IntegrationBase with API. Currently, the ecosystem is diverse. Overview of methods integrate is exported by Polynomi…

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## [Enzyme cannot deduce type for integral function in reverse mode AD](https://discourse.julialang.org/t/enzyme-cannot-deduce-type-for-integral-function-in-reverse-mode-ad/127822)

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**Author:** [@jwalker](https://discourse.julialang.org/u/jwalker)\
**Replies:** 11\
**Last updated:** [April 9, 2025, 4:06pm UTC](https://discourse.julialang.org/t/enzyme-cannot-deduce-type-for-integral-function-in-reverse-mode-ad/127822 "2025-04-09T16:06:04Z")

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Could someone explain why I’m getting the following error from this example? using Enzyme struct Parameters M::Int R::Real end function integrand2(v::Vector, nt::NamedTuple) x = v\[1\] y = v\[2\] θ = n…

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## [Integrating over piecewise approxfun](https://discourse.julialang.org/t/integrating-over-piecewise-approxfun/127309)

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**Author:** [@nilsbecker](https://discourse.julialang.org/u/nilsbecker)\
**Replies:** 8\
**Last updated:** [March 25, 2025, 4:08pm UTC](https://discourse.julialang.org/t/integrating-over-piecewise-approxfun/127309 "2025-03-25T16:08:26Z")

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Following up on my earlier post, I now have an ApproxFun.jl Fun defined over a piecewise domain: using ApproxFun f\_pw = Fun(x -\> (x \< 1.0 ? exp(x) : 1.), union(Segment(0.,1.), Segment(1.,2.))) f\_pw\_i = integrate(f\_pw) T…

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## [Symbolic Integration for hard expressions and generate function](https://discourse.julialang.org/t/symbolic-integration-for-hard-expressions-and-generate-function/124744)

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**Author:** [@MechRob](https://discourse.julialang.org/u/MechRob)\
**Replies:** 9\
**Last updated:** [January 22, 2025, 6:22pm UTC](https://discourse.julialang.org/t/symbolic-integration-for-hard-expressions-and-generate-function/124744 "2025-01-22T18:22:59Z")

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Hello All, I am trying to generate Julia functions by deriving the symbolic expressions in Julia. I started using Symbolics.jl and SymbolicNumericIntegration.jl, however it seems that SymbolicNumericIntegration.jl is no…

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## [Compute integral for DelaunayTriangulation.jl to be able to solve PDE with FiniteVolumeMethod.jl](https://discourse.julialang.org/t/compute-integral-for-delaunaytriangulation-jl-to-be-able-to-solve-pde-with-finitevolumemethod-jl/124310)

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**Author:** [@B4rtel](https://discourse.julialang.org/u/B4rtel)\
**Replies:** 4\
**Last updated:** [January 2, 2025, 3:20pm UTC](https://discourse.julialang.org/t/compute-integral-for-delaunaytriangulation-jl-to-be-able-to-solve-pde-with-finitevolumemethod-jl/124310 "2025-01-02T15:20:13Z")

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Hi :), I would like to solve a advection PDE of the form \\frac{\\partial}{\\partial t} f(x,t) = - \\nabla\_x \\cdot \\left(\\left(\\int \[\\phi(p\_1(x,y),\\phi(p\_2(x,y)\]\\odot (y-x) f(y,t) \\text{d} y\\right) f(x,t)\\right) for p\_a(x\_i…

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## [Integrate convolution symbolically to solve PDE](https://discourse.julialang.org/t/integrate-convolution-symbolically-to-solve-pde/123810)

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**Author:** [@B4rtel](https://discourse.julialang.org/u/B4rtel)\
**Replies:** 2\
**Last updated:** [December 13, 2024, 9:32pm UTC](https://discourse.julialang.org/t/integrate-convolution-symbolically-to-solve-pde/123810 "2024-12-13T21:32:41Z")

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I would like to solve a PDE with MethodOfLines.jl and ModellingToolkit.jl similar to the example docs.sciml.ai/MethodOfLines/stable/tutorials/PIDE/. My modification is to change the integral term. Instead of integrating …

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## [Integration on an ordered domain](https://discourse.julialang.org/t/integration-on-an-ordered-domain/118180)

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**Author:** [@IlliaFaraji](https://discourse.julialang.org/u/IlliaFaraji)\
**Replies:** 3\
**Last updated:** [August 14, 2024, 2:55pm UTC](https://discourse.julialang.org/t/integration-on-an-ordered-domain/118180 "2024-08-14T14:55:00Z")

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I want to carry out an integral of this form \\int\_{0}^{\\infty} \\int\_{0}^{t\_{n}} \\ldots \\int\_{0}^{t\_2} \\ f(s\_1, \\ldots, s\_n)\\, \\mathrm{d}s\_1 \\ldots \\mathrm{d}s\_n , for n \\approx 10. The domain of integration here is S=…

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## [Slow numerical integration of scalar function](https://discourse.julialang.org/t/slow-numerical-integration-of-scalar-function/114976)

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**Author:** [@golanor](https://discourse.julialang.org/u/golanor)\
**Replies:** 1\
**Last updated:** [May 30, 2024, 5:16pm UTC](https://discourse.julialang.org/t/slow-numerical-integration-of-scalar-function/114976 "2024-05-30T17:16:24Z")

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Hi, I’m trying to compute a set of integrals, and the integration takes a lot of time and allocates a lot. Is there a way to speed it up? MWE: using Integrals, BenchmarkTools const ω1, ω2 = 33.807, 37.822; const Ω1, …

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## [Integration packages to calculate the first N Fourier coefficients](https://discourse.julialang.org/t/integration-packages-to-calculate-the-first-n-fourier-coefficients/114787)

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**Author:** [@ccmejia](https://discourse.julialang.org/u/ccmejia)\
**Replies:** 3\
**Last updated:** [May 27, 2024, 6:54pm UTC](https://discourse.julialang.org/t/integration-packages-to-calculate-the-first-n-fourier-coefficients/114787 "2024-05-27T18:54:58Z")

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I am trying to calculate the first N Fourier coefficients for sampled data (harmonic + gaussian like). The Riemann sum was my first approach, however I think the results are not enough accurate. Therefore, I am trying t…

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## [QuadGK unexpected behavior on first degree polynomial](https://discourse.julialang.org/t/quadgk-unexpected-behavior-on-first-degree-polynomial/113134)

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**Author:** [@Domenico\_Lahaye](https://discourse.julialang.org/u/Domenico_Lahaye)\
**Replies:** 2\
**Last updated:** [April 18, 2024, 2:25pm UTC](https://discourse.julialang.org/t/quadgk-unexpected-behavior-on-first-degree-polynomial/113134 "2024-04-18T14:25:34Z")

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I constructed a tiny example on which my (naive?) use of the quadgk() fails. The example is a first order polynomial in x and y on the triangular domain with vertices (0,0), (1,0) and (0,1). Below a working and failing M…

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## [How to evaluate multivariate log normal distribution at arbitrary point?](https://discourse.julialang.org/t/how-to-evaluate-multivariate-log-normal-distribution-at-arbitrary-point/112608)

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**Author:** [@structural](https://discourse.julialang.org/u/structural)\
**Replies:** 2\
**Last updated:** [April 7, 2024, 9:46am UTC](https://discourse.julialang.org/t/how-to-evaluate-multivariate-log-normal-distribution-at-arbitrary-point/112608 "2024-04-07T09:46:47Z")

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Suppose I have the following distribution over two variables dist = MvLogNormal(mean\_a\_b, cov\_a\_b) Suppose h is an array of dimension 1000\\times 2. For each row of array h, the first entry represents the rank of the …

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## [Numerical integration over 3D domain of vector-valued function](https://discourse.julialang.org/t/numerical-integration-over-3d-domain-of-vector-valued-function/112284)

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**Author:** [@Lisette\_de\_Bruin](https://discourse.julialang.org/u/Lisette_de_Bruin)\
**Replies:** 33\
**Last updated:** [April 6, 2024, 6:52pm UTC](https://discourse.julialang.org/t/numerical-integration-over-3d-domain-of-vector-valued-function/112284 "2024-04-06T18:52:50Z")

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Hi all, I am interested in evaluating a volume integral of a vector-valued function. So the integral has the following form: I already tried to use nested quadgk and hcubature. Both methods give me the correct result…

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## [Why does "QuadGK.jl" not behave the same as "Integrals.jl with QuadGKJL()"](https://discourse.julialang.org/t/why-does-quadgk-jl-not-behave-the-same-as-integrals-jl-with-quadgkjl/110795)

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**Author:** [@Laura](https://discourse.julialang.org/u/Laura)\
**Replies:** 3\
**Last updated:** [February 29, 2024, 7:08am UTC](https://discourse.julialang.org/t/why-does-quadgk-jl-not-behave-the-same-as-integrals-jl-with-quadgkjl/110795 "2024-02-29T07:08:36Z")

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I am writing a program to perform a spherical Bessel transformation which requires some one dimensional integrals but I am having some trouble with the Integrals.jl package. Naturally my first attempt to do this was to …

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## [How to use autodiff with Quadrature.jl](https://discourse.julialang.org/t/how-to-use-autodiff-with-quadrature-jl/77437)

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**Author:** [@samerb](https://discourse.julialang.org/u/samerb)\
**Replies:** 4\
**Last updated:** [February 20, 2024, 7:47pm UTC](https://discourse.julialang.org/t/how-to-use-autodiff-with-quadrature-jl/77437 "2024-02-20T19:47:39Z")

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I’m trying to use autodiff on a function that uses Quadrature.jl numerical integration. I’m getting an error and not sure why. Any suggestions? Thanks. The function f(y) is \\int\_0^y x dx - y (computed numerically using …

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## [BatchIntegralFunction not appearing to work as intended](https://discourse.julialang.org/t/batchintegralfunction-not-appearing-to-work-as-intended/109513)

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**Author:** [@HSnowden](https://discourse.julialang.org/u/HSnowden)\
**Replies:** 2\
**Last updated:** [February 3, 2024, 4:05am UTC](https://discourse.julialang.org/t/batchintegralfunction-not-appearing-to-work-as-intended/109513 "2024-02-03T04:05:09Z")

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I am trying to implement a batch integral function using the new BatchIntegralFunction rather than then deprecated nout/batch keywords. However, when I do, the in-place vector to fill place the answer in is the incorrec…

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## [Is there any documentation on "IntegralFunctions"](https://discourse.julialang.org/t/is-there-any-documentation-on-integralfunctions/108970)

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**Author:** [@Laura](https://discourse.julialang.org/u/Laura)\
**Replies:** 8\
**Last updated:** [February 3, 2024, 12:36am UTC](https://discourse.julialang.org/t/is-there-any-documentation-on-integralfunctions/108970 "2024-02-03T00:36:50Z")

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I have been trying to solve two integrals at the same time using the Integrals.jl Package. I am following the example in the documentation of Integrals.jl in the link below. My function that I am integrating is an in-…

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## [Why does my cubature of ODESolution break down with finite limits?](https://discourse.julialang.org/t/why-does-my-cubature-of-odesolution-break-down-with-finite-limits/108736)

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**Author:** [@homocomputeris](https://discourse.julialang.org/u/homocomputeris)\
**Replies:** 18\
**Last updated:** [January 24, 2024, 11:04am UTC](https://discourse.julialang.org/t/why-does-my-cubature-of-odesolution-break-down-with-finite-limits/108736 "2024-01-24T11:04:34Z")

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I want to find the multi-dimensional integral of a scalar-valued function with vector argument defined on a rectangle (basically, product of truncated PDFs). The argument of the function comes from solving a system of OD…

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## [Guide to numerical integration methods?](https://discourse.julialang.org/t/guide-to-numerical-integration-methods/108704)

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**Author:** [@mike.ingold](https://discourse.julialang.org/u/mike.ingold)\
**Replies:** 10\
**Last updated:** [January 16, 2024, 11:03pm UTC](https://discourse.julialang.org/t/guide-to-numerical-integration-methods/108704 "2024-01-16T23:03:20Z")

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To pile on with a related question, as a EE without a particularly deep math background, @stevengj do you have any handy references for the different integration methods and their advantages/pitfalls? I find myself writ…

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## [Quadratures and cubatures with Dirac deltas](https://discourse.julialang.org/t/quadratures-and-cubatures-with-dirac-deltas/108683)

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**Author:** [@homocomputeris](https://discourse.julialang.org/u/homocomputeris)\
**Replies:** 11\
**Last updated:** [January 11, 2024, 6:46pm UTC](https://discourse.julialang.org/t/quadratures-and-cubatures-with-dirac-deltas/108683 "2024-01-11T18:46:46Z")

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Are there ways to compute cubatures of functions that include the Dirac delta function?

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## [How to improve the implementation of a function involving a numerical integration?](https://discourse.julialang.org/t/how-to-improve-the-implementation-of-a-function-involving-a-numerical-integration/105444)

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**Author:** [@lsablon](https://discourse.julialang.org/u/lsablon)\
**Replies:** 7\
**Last updated:** [October 27, 2023, 4:10am UTC](https://discourse.julialang.org/t/how-to-improve-the-implementation-of-a-function-involving-a-numerical-integration/105444 "2023-10-27T04:10:03Z")

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Hello, I am trying to optimize my code, but I don’t really know in which direction I should go (but I know I don’t want to use multithreading). Here is my goal: I want to implement the following function k\_\\perp(x,y;…

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## [QuadGK returns NaNs](https://discourse.julialang.org/t/quadgk-returns-nans/105308)

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**Author:** [@aner-sanchez](https://discourse.julialang.org/u/aner-sanchez)\
**Replies:** 4\
**Last updated:** [October 24, 2023, 1:24pm UTC](https://discourse.julialang.org/t/quadgk-returns-nans/105308 "2023-10-24T13:24:46Z")

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Hello everyone :slight\_smile: Would someone know why using QuadGK n = 538 \_, w, \_ = kronrod(n,1e-11,40); @show w returns a vector of NaN weights at n=538 and not before?

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## [How to compute integral of multivariate normal with bounds defined by lines](https://discourse.julialang.org/t/how-to-compute-integral-of-multivariate-normal-with-bounds-defined-by-lines/104160)

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**Author:** [@Christopher\_Fisher](https://discourse.julialang.org/u/Christopher_Fisher)\
**Replies:** 13\
**Last updated:** [September 25, 2023, 8:10am UTC](https://discourse.julialang.org/t/how-to-compute-integral-of-multivariate-normal-with-bounds-defined-by-lines/104160 "2023-09-25T08:10:16Z")

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Hi all, I would like to use Distributions.jl and HCubature.jl (or suitable alternative) to compute an integral over part of the domain of a multivariate normal distribution. The image below provides an example. In the i…

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## [Definition of an integral function whose argument is the upper limit of integration](https://discourse.julialang.org/t/definition-of-an-integral-function-whose-argument-is-the-upper-limit-of-integration/103946)

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**Author:** [@aburousan](https://discourse.julialang.org/u/aburousan)\
**Replies:** 2\
**Last updated:** [September 18, 2023, 2:01pm UTC](https://discourse.julialang.org/t/definition-of-an-integral-function-whose-argument-is-the-upper-limit-of-integration/103946 "2023-09-18T14:01:55Z")

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Hi, I want to define a function let’s say, $$ f(x) = \\int\_0^x u^2 du /(e^{u^2+16} +1)^{\\frac{3/2}}$$ How can I do this?, A naive approach is to use a loop and just each time calculate the whole thing. But is there any…

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## [How to evaluate a complex function between complex bounds](https://discourse.julialang.org/t/how-to-evaluate-a-complex-function-between-complex-bounds/102460)

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**Author:** [@AkchurinDA](https://discourse.julialang.org/u/AkchurinDA)\
**Replies:** 2\
**Last updated:** [August 3, 2023, 10:43pm UTC](https://discourse.julialang.org/t/how-to-evaluate-a-complex-function-between-complex-bounds/102460 "2023-08-03T22:43:21Z")

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I’m having trouble evaluating the following expression that contains an integral with a complex function with complex bounds. In this expression, \\phi() is the PDF of a standard normal distribution, \\beta is a number…

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## [Handling an overflow example in QuadGK](https://discourse.julialang.org/t/handling-an-overflow-example-in-quadgk/101657)

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**Author:** [@stevengj](https://discourse.julialang.org/u/stevengj)\
**Replies:** 5\
**Last updated:** [July 16, 2023, 2:06pm UTC](https://discourse.julialang.org/t/handling-an-overflow-example-in-quadgk/101657 "2023-07-16T14:06:11Z")

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Someone asked me this question over email, and I decided to post my answer here since it might be of more general interest. Suppose that we are trying to compute \\int\_0^\\infty (e^y - 1) \\frac{e^{-2.5y}}{y^{1.2}} dy. Th…

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