Optimal. Leaf size=12 \[ -\frac{x}{\left (b x^3\right )^{2/3}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.00673084, antiderivative size = 12, 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 \[ -\frac{x}{\left (b x^3\right )^{2/3}} \]
Antiderivative was successfully verified.
[In] Int[(b*x^3)^(-2/3),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 1.52953, size = 14, normalized size = 1.17 \[ - \frac{\sqrt [3]{b x^{3}}}{b x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*x**3)**(2/3),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00327759, size = 12, normalized size = 1. \[ -\frac{x}{\left (b x^3\right )^{2/3}} \]
Antiderivative was successfully verified.
[In] Integrate[(b*x^3)^(-2/3),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 11, normalized size = 0.9 \[ -{x \left ( b{x}^{3} \right ) ^{-{\frac{2}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b*x^3)^(2/3),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.44463, size = 14, normalized size = 1.17 \[ -\frac{x}{\left (b x^{3}\right )^{\frac{2}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3)^(-2/3),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.23482, size = 20, normalized size = 1.67 \[ -\frac{\left (b x^{3}\right )^{\frac{1}{3}}}{b x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3)^(-2/3),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.69686, size = 14, normalized size = 1.17 \[ - \frac{x}{b^{\frac{2}{3}} \left (x^{3}\right )^{\frac{2}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*x**3)**(2/3),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\left (b x^{3}\right )^{\frac{2}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3)^(-2/3),x, algorithm="giac")
[Out]