# Symbolic integration

**URL:** <https://discourse.julialang.org/t/symbolic-integration/32869>\
**Category:** New to Julia\
**Tags:** question, package\
**Created:** [January 2, 2020, 12:17pm UTC](https://discourse.julialang.org/t/symbolic-integration/32869 "2020-01-02T12:17:09Z")\
**Posts on this page:** 13\
**Page:** 1

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**Author:** ![Stephen](https://avatars.discourse-cdn.com/v4/letter/s/96bed5/32.png) [@Stephen](https://discourse.julialang.org/u/Stephen)\
**Post date:** [January 2, 2020, 12:17pm UTC](https://discourse.julialang.org/t/symbolic-integration/32869/1 "2020-01-02T12:17:09Z")

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Is there any recommend package to compute the integration of following？  
 ![image](https://global.discourse-cdn.com/julialang/original/3X/a/9/a9b1513242423143f3a8dfacd7387faffd5d13fe.png)

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**Author:** ![stevengj](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/stevengj/32/71_2.png) [@stevengj](https://discourse.julialang.org/u/stevengj)\
**Post date:** [January 2, 2020, 12:24pm UTC](https://discourse.julialang.org/t/symbolic-integration/32869/2 "2020-01-02T12:24:49Z")

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[SymPy](https://github.com/JuliaPy/SymPy.jl)?

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**Author:** ![Yifan\_Liu](https://avatars.discourse-cdn.com/v4/letter/y/4da419/32.png) [@Yifan\_Liu](https://discourse.julialang.org/u/Yifan_Liu)\
**Post date:** [April 30, 2020, 4:19am UTC](https://discourse.julialang.org/t/symbolic-integration/32869/3 "2020-04-30T04:19:22Z")

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Is there any other package other than SymPy.jl that could do symbolic integration?

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**Author:** ![Rob\_van\_Weelderen](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rob_van_weelderen/32/7621_2.png) [@Rob\_van\_Weelderen](https://discourse.julialang.org/u/Rob_van_Weelderen)\
**Post date:** [April 30, 2020, 11:57am UTC](https://discourse.julialang.org/t/symbolic-integration/32869/4 "2020-04-30T11:57:35Z")

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Try with [Reduce.jl](https://github.com/chakravala/Reduce.jl)

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**Author:** ![Yifan\_Liu](https://avatars.discourse-cdn.com/v4/letter/y/4da419/32.png) [@Yifan\_Liu](https://discourse.julialang.org/u/Yifan_Liu)\
**Post date:** [April 30, 2020, 2:41pm UTC](https://discourse.julialang.org/t/symbolic-integration/32869/5 "2020-04-30T14:41:23Z")

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I read the docs of Reduce.jl but it does not mention symbolic integration.

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**Author:** ![Rob\_van\_Weelderen](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rob_van_weelderen/32/7621_2.png) [@Rob\_van\_Weelderen](https://discourse.julialang.org/u/Rob_van_Weelderen)\
**Post date:** [April 30, 2020, 4:34pm UTC](https://discourse.julialang.org/t/symbolic-integration/32869/6 "2020-04-30T16:34:16Z")

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Better check the tutorials and books section of [reduce itself](https://reduce-algebra.sourceforge.io/books.php)

I only briefly used Reduce, and never the Julia interface package. So I’m afraid I can’t give you more help.

Good luck

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**Author:** ![brett\_knoss](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/brett_knoss/32/13050_2.png) [@brett\_knoss](https://discourse.julialang.org/u/brett_knoss)\
**Post date:** [November 10, 2020, 5:14pm UTC](https://discourse.julialang.org/t/symbolic-integration/32869/7 "2020-11-10T17:14:29Z")

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Does ModelingToolkit or SymbolicUtilities have symbolic integration, otherwise I would look at SymEngine, then SymPy. (Maxima and Reduce are neat, but they have issues when using Weave, and I don’t think, that LISP is much faster than Python).

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**Author:** ![brett\_knoss](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/brett_knoss/32/13050_2.png) [@brett\_knoss](https://discourse.julialang.org/u/brett_knoss)\
**Post date:** [February 22, 2021, 8:12pm UTC](https://discourse.julialang.org/t/symbolic-integration/32869/8 "2021-02-22T20:12:57Z")

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SymPy is your best option, although it can have problems. Maxima is good, but better in it’s GUI. Reduce has a lot of problems. Modelling Tookit is the best option for derivatives, but it can’t do integration at this time. I’ll be sure to keep you posted on this. @ChrisRackauckas is in charge of ModelingToolkit, so he can tell you more.

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**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [February 22, 2021, 9:47pm UTC](https://discourse.julialang.org/t/symbolic-integration/32869/9 "2021-02-22T21:47:12Z")

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MTK, not yet. I have some cool ideas but right now they are ideas

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**Author:** ![brett\_knoss](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/brett_knoss/32/13050_2.png) [@brett\_knoss](https://discourse.julialang.org/u/brett_knoss)\
**Post date:** [October 17, 2022, 2:12am UTC](https://discourse.julialang.org/t/symbolic-integration/32869/10 "2022-10-17T02:12:39Z")

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What is required for integration?

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**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [October 17, 2022, 6:34am UTC](https://discourse.julialang.org/t/symbolic-integration/32869/11 "2022-10-17T06:34:34Z")

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Just someone to do it. There is a symbolic integration now:

[https://docs.sciml.ai/SymbolicNumericIntegration/dev/](https://docs.sciml.ai/SymbolicNumericIntegration/dev/)

We should get more standard methods too though.

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<div class="post-metadata">

**Author:** ![brett\_knoss](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/brett_knoss/32/13050_2.png) [@brett\_knoss](https://discourse.julialang.org/u/brett_knoss)\
**Post date:** [November 22, 2023, 5:06am UTC](https://discourse.julialang.org/t/symbolic-integration/32869/12 "2023-11-22T05:06:43Z")

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I get a strange result

```julia
using Symbolics
using SymbolicNumericIntegration

E(x)=(x^(3/2)/a^2)*exp(-(x/(2*a^2))) # the function provided
F(X)=integrate(E(x^2),(x,0,Inf);symbolic=true , detailed=false)
print(F(x))

```

gives me

\begin{equation}

- \infty e^{\frac{-\infty}{2 a^{2}}} + 2.0 a^{2} - 2.0 a^{2} e^{\frac{-\infty}{2 a^{2}}}  
\end{equation}

sorry it’s in Tex, I can’t load a screenshot, but it’s not 2a^2 (I used a for theta)

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<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [November 22, 2023, 6:12am UTC](https://discourse.julialang.org/t/symbolic-integration/32869/13 "2023-11-22T06:12:37Z")

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open an issue