Thanks for the results! A side quest of mine was to find a solution of the form:
integral[integrand, t] = const + slope*t + periodic(t) Is this possible to instruct the CAS to bring it in this form? Now it seems Rubi and Mathematica dont show the result in this form. BTW: A slope is seen in this related problem: Problem: y' = cos(t) * (2 + cos(t)) / 100 Solution: y(t) = c_1 + t/200 + sin(t)/50 + 1/200 sin(t) cos(t) Nasser M. Abbasi schrieb am Samstag, 21. Oktober 2023 um 04:41:31 UTC+2: > Fyi, Rubi and Mathematica 13.3.1 gives answer in terms of Hypergeometric > special function. Not sure if you consider this one the "usual" special > functions you refer to: > > integrand=Cos[t]^(1/3)*(2+Cos[t])/100 > Integrate[integrand,t] > > -(1/1400)3 Cos[t]^(4/3) Csc[t] (7 > Hypergeometric2F1[1/2,2/3,5/3,Cos[t]^2]+2 Cos[t] > Hypergeometric2F1[1/2,7/6,13/6,Cos[t]^2]) Sqrt[Sin[t]^2] > > And Rubi gives > > Int[integrand,t] > -((3 Cos[t]^(4/3) Hypergeometric2F1[1/2,2/3,5/3,Cos[t]^2] Sin[t])/(200 > Sqrt[Sin[t]^2]))-(3 Cos[t]^(7/3) Hypergeometric2F1[1/2,7/6,13/6,Cos[t]^2] > Sin[t])/(700 Sqrt[Sin[t]^2]) > > Tried Maxima, Giac and Maple and these all can't solve this either. > --Nasser > > > On Friday, October 20, 2023 at 6:41:52 PM UTC-5 Waldek Hebisch wrote: > >> On Fri, Oct 20, 2023 at 02:21:21PM -0700, Mild Shock wrote: >> > Possible to make FriCAS solve this integral? >> > >> > /* Version: FriCAS 1.3.7, WSL2 */ >> > /* ^(1/3) is supposed to be the real root */ >> > >> > (2) -> integrate(cos(t)^(1/3)*(2+cos(t))/100, t) >> > >> > t 3+-------+ >> > ++ (cos(%A) + 2)\|cos(%A) >> > (2) | ----------------------- d%A >> > ++ 100 >> > >> >> Well, FriCAS claims tha answer is not elementary. Currently >> FriCAS can not find answer in terms of "usual" special >> functions and I do not know if there such an answer. >> >> Note that what is produced above can be treated as ad-hoc >> special function, so there is answer, the question is >> if this is more explicit or simpler answer. >> >> It is not clear what you mean by "Make it work"? If you >> know better answer you could use rewrite rule to change >> FriCAS result to a different one, but this is very limited in >> scope. Due to the way FriCAS integrator works there is no >> way to provide hints. >> >> If this integral is doable in terms of popular special functions, >> there is good chance that it will be handled in the future. >> But not in current version. >> >> -- >> Waldek Hebisch >> > -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/fricas-devel/183d9317-ee43-405f-89e3-a883c8c5f12dn%40googlegroups.com.
