Optimal. Leaf size=19 \[ \frac{a x^3}{3}+\frac{3}{8} b x^{8/3} \]
[Out]
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Rubi [A] time = 0.0160699, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{a x^3}{3}+\frac{3}{8} b x^{8/3} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x^(1/3))*x^2,x]
[Out]
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Rubi in Sympy [A] time = 2.93624, size = 15, normalized size = 0.79 \[ \frac{a x^{3}}{3} + \frac{3 b x^{\frac{8}{3}}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x**(1/3))*x**2,x)
[Out]
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Mathematica [A] time = 0.00454728, size = 19, normalized size = 1. \[ \frac{a x^3}{3}+\frac{3}{8} b x^{8/3} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x^(1/3))*x^2,x]
[Out]
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Maple [A] time = 0.002, size = 14, normalized size = 0.7 \[{\frac{3\,b}{8}{x}^{{\frac{8}{3}}}}+{\frac{a{x}^{3}}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^(1/3))*x^2,x)
[Out]
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Maxima [A] time = 1.42558, size = 20, normalized size = 1.05 \[ \frac{1}{24} \,{\left (8 \, a + \frac{9 \, b}{x^{\frac{1}{3}}}\right )} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))*x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.223526, size = 18, normalized size = 0.95 \[ \frac{1}{3} \, a x^{3} + \frac{3}{8} \, b x^{\frac{8}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))*x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.38101, size = 15, normalized size = 0.79 \[ \frac{a x^{3}}{3} + \frac{3 b x^{\frac{8}{3}}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x**(1/3))*x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.217181, size = 18, normalized size = 0.95 \[ \frac{1}{3} \, a x^{3} + \frac{3}{8} \, b x^{\frac{8}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))*x^2,x, algorithm="giac")
[Out]