Optimal. Leaf size=34 \[ \frac{a^2 x^2}{2}+\frac{6}{7} a b x^{7/3}+\frac{3}{8} b^2 x^{8/3} \]
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Rubi [A] time = 0.0542323, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{a^2 x^2}{2}+\frac{6}{7} a b x^{7/3}+\frac{3}{8} b^2 x^{8/3} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^(1/3))^2*x,x]
[Out]
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Rubi in Sympy [A] time = 8.03824, size = 31, normalized size = 0.91 \[ \frac{a^{2} x^{2}}{2} + \frac{6 a b x^{\frac{7}{3}}}{7} + \frac{3 b^{2} x^{\frac{8}{3}}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/3))**2*x,x)
[Out]
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Mathematica [A] time = 0.0102203, size = 34, normalized size = 1. \[ \frac{a^2 x^2}{2}+\frac{6}{7} a b x^{7/3}+\frac{3}{8} b^2 x^{8/3} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^(1/3))^2*x,x]
[Out]
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Maple [A] time = 0.002, size = 25, normalized size = 0.7 \[{\frac{{a}^{2}{x}^{2}}{2}}+{\frac{6\,ab}{7}{x}^{{\frac{7}{3}}}}+{\frac{3\,{b}^{2}}{8}{x}^{{\frac{8}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/3))^2*x,x)
[Out]
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Maxima [A] time = 1.44189, size = 132, normalized size = 3.88 \[ \frac{3 \,{\left (b x^{\frac{1}{3}} + a\right )}^{8}}{8 \, b^{6}} - \frac{15 \,{\left (b x^{\frac{1}{3}} + a\right )}^{7} a}{7 \, b^{6}} + \frac{5 \,{\left (b x^{\frac{1}{3}} + a\right )}^{6} a^{2}}{b^{6}} - \frac{6 \,{\left (b x^{\frac{1}{3}} + a\right )}^{5} a^{3}}{b^{6}} + \frac{15 \,{\left (b x^{\frac{1}{3}} + a\right )}^{4} a^{4}}{4 \, b^{6}} - \frac{{\left (b x^{\frac{1}{3}} + a\right )}^{3} a^{5}}{b^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^2*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212494, size = 32, normalized size = 0.94 \[ \frac{3}{8} \, b^{2} x^{\frac{8}{3}} + \frac{6}{7} \, a b x^{\frac{7}{3}} + \frac{1}{2} \, a^{2} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^2*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.30568, size = 31, normalized size = 0.91 \[ \frac{a^{2} x^{2}}{2} + \frac{6 a b x^{\frac{7}{3}}}{7} + \frac{3 b^{2} x^{\frac{8}{3}}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/3))**2*x,x)
[Out]
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GIAC/XCAS [A] time = 0.258597, size = 32, normalized size = 0.94 \[ \frac{3}{8} \, b^{2} x^{\frac{8}{3}} + \frac{6}{7} \, a b x^{\frac{7}{3}} + \frac{1}{2} \, a^{2} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^2*x,x, algorithm="giac")
[Out]