email@example.com schrieb: > > M> I suspect you have > M> tried the SymPy integrator on the integrals too, but in view of the > M> results decided to remain silent. > > Exactly. Moreover, they know what the state of things is and they are > working on it. > > What they do probably not know is how buggy the interface Sage/Maxima > really is. 7 run-time errors! This is not excusable. >
To me these bugs appear to be internal to Maxima, not just interfacing problems. Some remarks on your model antiderivatives for the integrals from Timofeev's chapter 1:
In the model evaluation of integrals 3 and 5 you prefer LN(COT) whereas for numbers 4, 60 and 76 you write LN((1 - COS)/(1 + COS)). In number 18 you prefer the shorter but discontinuous antiderivative ATAN(2*TAN(x)/ SQRT(3)) whereas you opted for the continuous x - ATAN(3*SIN(x)*COS(x)/ (SQRT(10) + 2 + 3*COS(x)^2)) in the similar case of number 61. In number 27 you express the antiderivative as ATANH + LN whereas in the similar case of number 46 you express it as LN + LN instead. As noted in the original thread, your compact evaluation 1/2*ASIN(x^2/a^2) of integral 50 is not valid for a general complex parameter a. In my file I have converted the LN antiderivatives of problems 58 and 83 to shorter ATANH versions. For integral 63 I am using the less compact evaluation 1/2*LN((1 + TAN(x))/(1 - TAN(x))) because it avoids jumps at +- pi/2.
The integral numbers in the above are those used on your site. For easy reference my (current) Derive file is appended, where the numbering is Timofeev's however.
That Maxima succeeds on integrals 10 and 11 from Timofeev's chapter 7 shows the use of Risch integration I think.