Optimal. Leaf size=34 \[ \frac{a^2 x^3}{3}+\frac{3}{4} a b x^{8/3}+\frac{3}{7} b^2 x^{7/3} \]
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Rubi [A] time = 0.064753, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ \frac{a^2 x^3}{3}+\frac{3}{4} a b x^{8/3}+\frac{3}{7} b^2 x^{7/3} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x^(1/3))^2*x^2,x]
[Out]
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Rubi in Sympy [A] time = 9.85524, size = 31, normalized size = 0.91 \[ \frac{a^{2} x^{3}}{3} + \frac{3 a b x^{\frac{8}{3}}}{4} + \frac{3 b^{2} x^{\frac{7}{3}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x**(1/3))**2*x**2,x)
[Out]
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Mathematica [A] time = 0.0157086, size = 34, normalized size = 1. \[ \frac{a^2 x^3}{3}+\frac{3}{4} a b x^{8/3}+\frac{3}{7} b^2 x^{7/3} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x^(1/3))^2*x^2,x]
[Out]
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Maple [A] time = 0.001, size = 25, normalized size = 0.7 \[{\frac{3\,{b}^{2}}{7}{x}^{{\frac{7}{3}}}}+{\frac{3\,ab}{4}{x}^{{\frac{8}{3}}}}+{\frac{{x}^{3}{a}^{2}}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^(1/3))^2*x^2,x)
[Out]
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Maxima [A] time = 1.43734, size = 35, normalized size = 1.03 \[ \frac{1}{84} \,{\left (28 \, a^{2} + \frac{63 \, a b}{x^{\frac{1}{3}}} + \frac{36 \, b^{2}}{x^{\frac{2}{3}}}\right )} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))^2*x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.219427, size = 32, normalized size = 0.94 \[ \frac{1}{3} \, a^{2} x^{3} + \frac{3}{4} \, a b x^{\frac{8}{3}} + \frac{3}{7} \, b^{2} x^{\frac{7}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))^2*x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.39865, size = 31, normalized size = 0.91 \[ \frac{a^{2} x^{3}}{3} + \frac{3 a b x^{\frac{8}{3}}}{4} + \frac{3 b^{2} x^{\frac{7}{3}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x**(1/3))**2*x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.21014, size = 32, normalized size = 0.94 \[ \frac{1}{3} \, a^{2} x^{3} + \frac{3}{4} \, a b x^{\frac{8}{3}} + \frac{3}{7} \, b^{2} x^{\frac{7}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))^2*x^2,x, algorithm="giac")
[Out]