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)
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