Introduction

These are ﬁrst 10 integrals from Kevin Charlwood’s 2008 article "Integration on Computer Algebra Systems" solved using diﬀerent CAS systems.

The original post on this topic is sci.math.symbolic by Martin

These are the CAS systems used

- Maple 2020 on windows 10 (64 bit)
- Mathematica 12.1 on windows 10
- Rubi 4.16.1
- Maxima 5.43.2 on Linux
- FriCAS 1.3.6 on Linux
- Sympy 1.5 under Python 3.7.3 using Anaconda distribution.
- mupad engine in Matlab 2016a symbolic toolbox
- Giac/Xcas 1.5.0.87-1 on Linux.

Summary of result

The following is summary of results for each integral. Result with a () around it means the antiderivative contains either a complex number on non-elementary function.

system | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | score |

FriCAS | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | 100% |

Maple | ✓ | ✓ | ✓ | ✓ | (✓) | ✓ | ✓ | ✓ | ✓ | ✓ | 100% |

Mathematica | ✓ | ✓ | ✓ | ✓ | (✓) | ✓ | ✓ | (✓) | (✓) | ✓ | 100% |

Rubi | ✓ | ✓ | ✗ | ✓ | (✓) | ✓ | ✓ | ✓ | ✓ | ✓ | 90% |

xCas | ✓ | ✓ | ✗ | ✓ | ✗ | ✓ | ✓ | (✓) | ✓ | ✓ | 80% |

Maxima | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✓ | ✗ | ✓ | ✗ | 40% |

Sympy | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | 30% |

mupad 2016a | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✓ | ✗ | 20% |

Downloads, references and links

- copy of Kevin Charlwood’s 2008 paper in PDF
- CharlwoodIntegrationProblems.pdf PDF ﬁle showing the 50 integrals and the best antiderivatives expected to each. By Albert Rich.