Mathematica vs 2022 MIT Integration Bee Qualifying Exam

Ideas
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2 Likes
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I would like to mention that there is a lot of theory behind finding the simplest form of an integral.

3

For example the function IntegrateAlgebraic uses many different heuristics to try to find the best form of a integral, but its a very challenging problem.
I might have been able to resolve some of the challenging problems with IntegrateAlgebraic, which uses Laurent Series for example to compute the simplest expansion in terms of elementary functions.

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Stephen Wolfram writes about the advances Mathematica has made in his blog post “Don’t Forget Integrals!” for 13.0.
I think its exciting to be able to simplify an integral that was previously expressible only in terms of elliptic integrals into ArcTanh, for example.

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I started working through the regular season problems.

Open in Wolfram Cloud ↗
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I would like to share how I got the correct answer to #3 on the 2022 qualifying exam. I set $MaxPiecewiseCases to 10000 and then

\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(2022\)]\(\((
\*SuperscriptBox[\(x\), \(2\)] - \[LeftFloor]x\[RightFloor] \
\[LeftCeiling]x\[RightCeiling])\) \[DifferentialD]x\)\)

worked to output 674.
Edit: I didn’t realize I already solved this in my first post.