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Topic: error in an integral, Rubi 4.3, QuotientOfLinearsParts error
Replies: 10   Last Post: Dec 9, 2013 5:44 PM

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Albert D. Rich

Posts: 311
From: Hawaii Island
Registered: 5/30/09
Re: error in an integral, Rubi 4.3, QuotientOfLinearsParts error
Posted: Dec 6, 2013 6:51 PM
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On Friday, November 29, 2013 3:34:13 PM UTC-10, Nasser M. Abbasi wrote:

> Rubi 4.3, Mathematica 9.02, windows 7
> -------------------------
> ClearAll[t]
> Assuming[t>0,
> Int[Sqrt[1+40 t] Sqrt[1+(162 t^2)/(4-2 I Sqrt[77])] Sqrt[1+(162 t^2)/(4+2 I Sqrt[77])],t]]
> ------------------------
> gives
> $RecursionLimit::reclim: Recursion depth of 1024 exceeded. >>

Hello Nasser,

Thank you for pointing out this infinite-recursion bug in Rubi 4.3 and earlier versions. A simpler example of the same bug is

Assuming[t>0, Int[Sqrt[(I+1)*(1+t+t^4)], t]]

It occurs when t>0 because Rubi uses algebraic simplification to transform the problem to

Assuming[t>0, Int[Sqrt[I+1]*Sqrt[1+t+t^4], t]]

But then Mathematica simplifies the integrand back to the original one before Rubi has a chance to pull out the constant factor Sqrt[I+1], thereby resulting in a classic case of infinite-recursion.

The just released version 4.4 of Rubi resolves the bug by splitting the factors of the square-root and pulling the resulting constant factor out of the integrand in a single step, yielding the guaranteed simpler problem

Assuming[t>0, Sqrt[I+1]*Int[Sqrt[1+t+t^4], t]]

An executable version of Rubi 4.4 and formatted pdf files of its newly revised rules are available for viewing and/or downloading at

Note that Rubi 4.4 is still not able to find a closed-form antiderivative for the above integrand or for your example.


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