Optimal. Leaf size=47 \[ \frac{a^3 x^3}{3}+\frac{9}{10} a^2 b x^{10/3}+\frac{9}{11} a b^2 x^{11/3}+\frac{b^3 x^4}{4} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.074644, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{a^3 x^3}{3}+\frac{9}{10} a^2 b x^{10/3}+\frac{9}{11} a b^2 x^{11/3}+\frac{b^3 x^4}{4} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^(1/3))^3*x^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 11.6034, size = 42, normalized size = 0.89 \[ \frac{a^{3} x^{3}}{3} + \frac{9 a^{2} b x^{\frac{10}{3}}}{10} + \frac{9 a b^{2} x^{\frac{11}{3}}}{11} + \frac{b^{3} x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/3))**3*x**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0120432, size = 41, normalized size = 0.87 \[ \frac{1}{660} x^3 \left (220 a^3+594 a^2 b \sqrt [3]{x}+540 a b^2 x^{2/3}+165 b^3 x\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^(1/3))^3*x^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 36, normalized size = 0.8 \[{\frac{{a}^{3}{x}^{3}}{3}}+{\frac{9\,{a}^{2}b}{10}{x}^{{\frac{10}{3}}}}+{\frac{9\,a{b}^{2}}{11}{x}^{{\frac{11}{3}}}}+{\frac{{b}^{3}{x}^{4}}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/3))^3*x^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.45569, size = 201, normalized size = 4.28 \[ \frac{{\left (b x^{\frac{1}{3}} + a\right )}^{12}}{4 \, b^{9}} - \frac{24 \,{\left (b x^{\frac{1}{3}} + a\right )}^{11} a}{11 \, b^{9}} + \frac{42 \,{\left (b x^{\frac{1}{3}} + a\right )}^{10} a^{2}}{5 \, b^{9}} - \frac{56 \,{\left (b x^{\frac{1}{3}} + a\right )}^{9} a^{3}}{3 \, b^{9}} + \frac{105 \,{\left (b x^{\frac{1}{3}} + a\right )}^{8} a^{4}}{4 \, b^{9}} - \frac{24 \,{\left (b x^{\frac{1}{3}} + a\right )}^{7} a^{5}}{b^{9}} + \frac{14 \,{\left (b x^{\frac{1}{3}} + a\right )}^{6} a^{6}}{b^{9}} - \frac{24 \,{\left (b x^{\frac{1}{3}} + a\right )}^{5} a^{7}}{5 \, b^{9}} + \frac{3 \,{\left (b x^{\frac{1}{3}} + a\right )}^{4} a^{8}}{4 \, b^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^3*x^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.212257, size = 47, normalized size = 1. \[ \frac{1}{4} \, b^{3} x^{4} + \frac{9}{11} \, a b^{2} x^{\frac{11}{3}} + \frac{9}{10} \, a^{2} b x^{\frac{10}{3}} + \frac{1}{3} \, a^{3} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^3*x^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 2.38298, size = 42, normalized size = 0.89 \[ \frac{a^{3} x^{3}}{3} + \frac{9 a^{2} b x^{\frac{10}{3}}}{10} + \frac{9 a b^{2} x^{\frac{11}{3}}}{11} + \frac{b^{3} x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/3))**3*x**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.21941, size = 47, normalized size = 1. \[ \frac{1}{4} \, b^{3} x^{4} + \frac{9}{11} \, a b^{2} x^{\frac{11}{3}} + \frac{9}{10} \, a^{2} b x^{\frac{10}{3}} + \frac{1}{3} \, a^{3} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^3*x^2,x, algorithm="giac")
[Out]