Hi I was unable to get zero out of (3) , so I tried a trick in (4) (Waldek once wrote that integrate simplifies its input), but (4) is now positive for all positive a,b,x ...
I'm confused... Riccardo (1) -> integrand:=1/(x^3*(a+b*x/sqrt(3))^(1/3)) 3┌─┐ \│3 (1) ─────────────────── ┌─────────────┐ 3 3│ ┌─┐ x \│b x\│3 + 3 a Type: Expression(Integer) (2) -> primitive:=integrate(integrand,x) 6┌─┐2 \│3 (2) - ──────────────────────── ┌───────────────┐2 2 3│ 6┌─┐3 2 x \│b x \│3 + 3 a Type: Union(Expression(Integer),...) (3) -> shouldBeZero := D(primitive,x) - integrand (3) ┌───────────────┐2 3┌─┐6┌─┐3 3┌─┐ 3│ 6┌─┐3 (- 3 b x\│3 \│3 - 9 a\│3 )\│b x \│3 + 3 a + ┌─────────────┐ 6┌─┐5 6┌─┐2 3│ ┌─┐ (4 b x \│3 + 9 a \│3 )\│b x\│3 + 3 a / ┌─────────────┐ ┌───────────────┐2 4 6┌─┐3 3 3│ ┌─┐ 3│ 6┌─┐3 (3 b x \│3 + 9 a x )\│b x\│3 + 3 a \│b x \│3 + 3 a Type: Expression(Integer) (4) -> shouldBeZero2:=eval(integrate(shouldBeZero,z),z=1) (4) 6┌─┐5 b \│3 ───────────────────────────────────────────────────────────────────────────── ┌───────────────┐2 3 5 2 3 6┌─┐3 2 4 3 2 3│ 6┌─┐3 ((9 b x + (27 a + 18 a)b x )\│3 + 27 a b x + 81 a x )\│b x \│3 + 3 a Type: Expression(Integer) -- 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 fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.