Hi Paolo, thanks for your interest in Maxima. From what you were saying on Stack Overflow, it sounds like Maxima returns a different representation of the antiderivative but it is valid. Is there reason to think Maxima's result is invalid?
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
actually, by calculating the derivative of the antiderivative and subtracting it to the function itself, as you suggested, it returns zero, after proper simplification. Hence, I would say that Maxima's result is valid. I've been influenced by the results indicated on the table of integrals and obtained with Wolfram Alpha, so I was uncertain about what I got with Maxima, but it was only a different representation. Sorry for not checking the correctness of Maxima results more thoroughly before posting the question on Stack Overflow as well as this bug report.
Nevertheless, I didn't manage to obtain with Maxima that:
asin(x/a) = atan(x/sqrt(a^2-x^2))
but this is a minor issue, in my opinion.
In addition, referring to my Stack Overflow question, an apparently weird result is obtained also with Sympy (even weirder, actually), though not of your interest as a Maxima developer, I guess. Therefore the post is still open for Sympy users/developers.
I really thank you for your time.
Paolo
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
Hi Paolo, I've marked this ticket as "not a bug" since the different antiderivatives are not incorrect. Also, ideally Maxima would know the identity about asin and atan but its absence is also not a bug. If you want to follow up specifically about the identity, you could post an item on the feature requests tracker: https://sourceforge.net/p/maxima/feature-requests/
Thanks again, and all the best. Robert.
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
Hi Paolo, thanks for your interest in Maxima. From what you were saying on Stack Overflow, it sounds like Maxima returns a different representation of the antiderivative but it is valid. Is there reason to think Maxima's result is invalid?
Hi Robert,
actually, by calculating the derivative of the antiderivative and subtracting it to the function itself, as you suggested, it returns zero, after proper simplification. Hence, I would say that Maxima's result is valid. I've been influenced by the results indicated on the table of integrals and obtained with Wolfram Alpha, so I was uncertain about what I got with Maxima, but it was only a different representation. Sorry for not checking the correctness of Maxima results more thoroughly before posting the question on Stack Overflow as well as this bug report.
Nevertheless, I didn't manage to obtain with Maxima that:
asin(x/a) = atan(x/sqrt(a^2-x^2))
but this is a minor issue, in my opinion.
In addition, referring to my Stack Overflow question, an apparently weird result is obtained also with Sympy (even weirder, actually), though not of your interest as a Maxima developer, I guess. Therefore the post is still open for Sympy users/developers.
I really thank you for your time.
Paolo
Hi Paolo, I've marked this ticket as "not a bug" since the different antiderivatives are not incorrect. Also, ideally Maxima would know the identity about asin and atan but its absence is also not a bug. If you want to follow up specifically about the identity, you could post an item on the feature requests tracker: https://sourceforge.net/p/maxima/feature-requests/
Thanks again, and all the best. Robert.