The antiderivative of a sum multiplies its terms' piecewise cases
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This is a symbolic integration problem in the C# library AngouriMath; the payload names no files or tests. Start by reproducing the three integrands from the table and comparing the printed antiderivatives, then trace how the integrator combines piecewise results for a sum. Done would mean the sum's answer is no longer the cross-product of the term cases, which is open-ended design work.
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描述
Part of #718
When two terms each integrate to a piecewise answer in the signs of the constants, the antiderivative of their sum lists every combination of cases, not one piecewise answer per term. Measured on master ed821bf3:
| Integrand | Answer |
|---|---|
1/(b*x^2 + m) |
287 chars |
1/(sqrt(a + b*x^2)*(b*x^2 + m)) |
685 chars |
1/(b*x^2 + m) - 1/(sqrt(a + b*x^2)*(b*x^2 + m)) |
3,685 chars |
The answer for the sum is almost four times the two pieces together.
#1873 meets this. Its conjugate splits 1/(a c + b c x^2 + d sqrt(a + b x^2)) into two such pieces and answers in 3,464 characters, and Rubi's 1.3.2:752 comes to 5,052. The answers are right; I checked them exactly at 50 and 2,000 digits. They are just much longer than they need to be.
What I'd expect: the sum of two piecewise answers stays a sum of two piecewise answers, unless the cases are merged where their conditions coincide.
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