Optimal. Leaf size=14 \[ \frac{3}{7} x \left (b x^2\right )^{2/3} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.00718682, 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 \[ \frac{3}{7} x \left (b x^2\right )^{2/3} \]
Antiderivative was successfully verified.
[In] Int[(b*x^2)^(2/3),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 1.26672, size = 12, normalized size = 0.86 \[ \frac{3 x \left (b x^{2}\right )^{\frac{2}{3}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2)**(2/3),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00208693, size = 14, normalized size = 1. \[ \frac{3}{7} x \left (b x^2\right )^{2/3} \]
Antiderivative was successfully verified.
[In] Integrate[(b*x^2)^(2/3),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 11, normalized size = 0.8 \[{\frac{3\,x}{7} \left ( b{x}^{2} \right ) ^{{\frac{2}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2)^(2/3),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43286, size = 14, normalized size = 1. \[ \frac{3}{7} \, \left (b x^{2}\right )^{\frac{2}{3}} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2)^(2/3),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.218329, size = 18, normalized size = 1.29 \[ \frac{3 \, b x^{3}}{7 \, \left (b x^{2}\right )^{\frac{1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2)^(2/3),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.85381, size = 15, normalized size = 1.07 \[ \frac{3 b^{\frac{2}{3}} x \left (x^{2}\right )^{\frac{2}{3}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2)**(2/3),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \left (b x^{2}\right )^{\frac{2}{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2)^(2/3),x, algorithm="giac")
[Out]