Optimal. Leaf size=14 \[ \frac{x}{2 \sqrt [3]{\frac{b}{x^3}}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0064643, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ \frac{x}{2 \sqrt [3]{\frac{b}{x^3}}} \]
Antiderivative was successfully verified.
[In] Int[(b/x^3)^(-1/3),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{x^{2} \left (\frac{b}{x^{3}}\right )^{\frac{2}{3}} \int x\, dx}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b/x**3)**(1/3),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00306992, size = 14, normalized size = 1. \[ \frac{x}{2 \sqrt [3]{\frac{b}{x^3}}} \]
Antiderivative was successfully verified.
[In] Integrate[(b/x^3)^(-1/3),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.001, size = 11, normalized size = 0.8 \[{\frac{x}{2}{\frac{1}{\sqrt [3]{{\frac{b}{{x}^{3}}}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b/x^3)^(1/3),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43781, size = 14, normalized size = 1. \[ \frac{x}{2 \, \left (\frac{b}{x^{3}}\right )^{\frac{1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b/x^3)^(-1/3),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.214957, size = 20, normalized size = 1.43 \[ \frac{x^{4} \left (\frac{b}{x^{3}}\right )^{\frac{2}{3}}}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b/x^3)^(-1/3),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.54985, size = 15, normalized size = 1.07 \[ \frac{x}{2 \sqrt [3]{b} \sqrt [3]{\frac{1}{x^{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b/x**3)**(1/3),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\left (\frac{b}{x^{3}}\right )^{\frac{1}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b/x^3)^(-1/3),x, algorithm="giac")
[Out]