The integration test suite consists of over 50 thousand problems involving rational functions, algebraic functions, elementary functions and special functions. Its creation was done in parallel with the implementation of Rubi. As rules were added to Rubi, problems that exercised every aspect of the new rules were added to the test suite.
These files contrast the results produced by Rubi with those produced by Mathematica 10's and Maple 18's built-in integrators on a small, but representative sample of these problems. Since Rubi was developed in conjunction with the test suite, its good performance is to be expected. And no doubt there are many problems Rubi is unable to integrate. Still, the favorable comparison with the commercial integrators remains valid for the numerous problems presented here.
The test results highlights are organized based on the expression type of the integrand. To view a PDF file or download a Mathematica notebook file of the highlights, click on one of the following integrand types:
Integration problems are highlighted in light gray. Following each is the result of evaluating the problem by the integrator in question. Preceding each is a caption giving the integrator used and the significance of the result. Note that the Maple results were manually converted into Mathematica syntax. The complete raw integration test results as generated by the three systems are available from the Rubi homepage.
The test suite was also conducted on these and other systems independently by Nasser M. Abbasi. The results, including numerous statistics and probability distributions, are posted at Computer Algebra Independent Integration Tests.