Optimal. Leaf size=19 \[ \frac{a x^2}{2}+\frac{3}{7} b x^{7/3} \]
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Rubi [A] time = 0.0161281, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{a x^2}{2}+\frac{3}{7} b x^{7/3} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^(1/3))*x,x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ a \int x\, dx + \frac{3 b x^{\frac{7}{3}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/3))*x,x)
[Out]
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Mathematica [A] time = 0.00493222, size = 19, normalized size = 1. \[ \frac{a x^2}{2}+\frac{3}{7} b x^{7/3} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^(1/3))*x,x]
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Maple [A] time = 0.002, size = 14, normalized size = 0.7 \[{\frac{a{x}^{2}}{2}}+{\frac{3\,b}{7}{x}^{{\frac{7}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/3))*x,x)
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Maxima [A] time = 1.43855, size = 132, normalized size = 6.95 \[ \frac{3 \,{\left (b x^{\frac{1}{3}} + a\right )}^{7}}{7 \, b^{6}} - \frac{5 \,{\left (b x^{\frac{1}{3}} + a\right )}^{6} a}{2 \, b^{6}} + \frac{6 \,{\left (b x^{\frac{1}{3}} + a\right )}^{5} a^{2}}{b^{6}} - \frac{15 \,{\left (b x^{\frac{1}{3}} + a\right )}^{4} a^{3}}{2 \, b^{6}} + \frac{5 \,{\left (b x^{\frac{1}{3}} + a\right )}^{3} a^{4}}{b^{6}} - \frac{3 \,{\left (b x^{\frac{1}{3}} + a\right )}^{2} a^{5}}{2 \, b^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.210685, size = 18, normalized size = 0.95 \[ \frac{3}{7} \, b x^{\frac{7}{3}} + \frac{1}{2} \, a x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.20788, size = 15, normalized size = 0.79 \[ \frac{a x^{2}}{2} + \frac{3 b x^{\frac{7}{3}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/3))*x,x)
[Out]
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GIAC/XCAS [A] time = 0.248049, size = 18, normalized size = 0.95 \[ \frac{3}{7} \, b x^{\frac{7}{3}} + \frac{1}{2} \, a x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)*x,x, algorithm="giac")
[Out]