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/2ebb3f63-d2e4-42b7-b3a5-9c1c6094777en%40googlegroups.com.
