# Symbolic integration

Is there any recommend package to compute the integration of following？

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

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Try with Reduce.jl

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

Better check the tutorials and books section of reduce itself

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

Good luck

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

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What is required for integration?

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

https://docs.sciml.ai/SymbolicNumericIntegration/dev/

We should get more standard methods too though.

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I get a strange result

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

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

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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