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#195 indefinite integral result contains unneeded constant of integration
I am calculating an integral to compute view factors for radiation heat transfer: when I define the integrand
d2F12_rec_x:(d^2*((x-ξ)/((2*d^2+2*c_1^2)*ξ^2+(-(4*d^2)-4*c_1^2)*x*ξ+(2*d^2+2*c_1^2)*x^2+2*d^4+4*c_1^2*d^2+2*c_1^4)+atan((2*x-2*ξ)/(2*sqrt(d^2+c_1^2)))/(2*(d^2+c_1^2)^(3/2))))/%pi
where d, c_1 are constants
and I integrate along ξ doing:
d2F12_rec_xξ: integrate(d2F12_rec_x, ξ)
the result is, after simplifying with logcontract:
-(((2·d^2·ξ-2·d^2·x)·atan((ξ-x)/sqrt(d^2+c_1^2))+d^2·sqrt(d^2+c_1^2)·log(d^2+c_1^2))/(sqrt(d^2+c_1^2)·(4·π·d^2+4·π·c_1^2)))
The logarithm term should'nt appear, according to the theory
https://arc.aiaa.org/doi/10.2514/3.11587
. I checked the theoretical result with wolfram alpha and it also didn't include the log term
thank you for your time
Fix up formulas
If I do
ratsimp(diff(d2F12_rec_xξ, ξ)-d2F12_rec_x),algebraic, I get 0 as the result. I think the integral is correct. It's just different from what Wolfram says. Since the log term is independent ofξ, I guess it's just a different constant of integration.Andres, thanks for taking the time to make a report. I'm marking this ticket as "not a bug", since it appears that the result is correct; it differs from the expected result by just a constant.
I agree the presence of the extra constant is suboptimal. I think it's reasonable to think about ways to detect constant terms that could be omitted. That would be a new feature for the indefinite integration code. As such I will move this ticket to the feature requests tracker.
Ticket moved from /p/maxima/bugs/4610/
Moving this ticket to the feature requests tracker. The new feature would be detecting a constant of integration which can be omitted from the result.