Optimal. Leaf size=16 \[ -\frac{1}{6 b \left (a+b x^3\right )^2} \]
[Out]
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Rubi [A] time = 0.00903664, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{1}{6 b \left (a+b x^3\right )^2} \]
Antiderivative was successfully verified.
[In] Int[x^2/(a + b*x^3)^3,x]
[Out]
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Rubi in Sympy [A] time = 2.19093, size = 14, normalized size = 0.88 \[ - \frac{1}{6 b \left (a + b x^{3}\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/(b*x**3+a)**3,x)
[Out]
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Mathematica [A] time = 0.00865362, size = 16, normalized size = 1. \[ -\frac{1}{6 b \left (a+b x^3\right )^2} \]
Antiderivative was successfully verified.
[In] Integrate[x^2/(a + b*x^3)^3,x]
[Out]
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Maple [A] time = 0.002, size = 15, normalized size = 0.9 \[ -{\frac{1}{6\,b \left ( b{x}^{3}+a \right ) ^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/(b*x^3+a)^3,x)
[Out]
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Maxima [A] time = 1.42751, size = 19, normalized size = 1.19 \[ -\frac{1}{6 \,{\left (b x^{3} + a\right )}^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(b*x^3 + a)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.242473, size = 35, normalized size = 2.19 \[ -\frac{1}{6 \,{\left (b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(b*x^3 + a)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.11547, size = 27, normalized size = 1.69 \[ - \frac{1}{6 a^{2} b + 12 a b^{2} x^{3} + 6 b^{3} x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2/(b*x**3+a)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.219005, size = 19, normalized size = 1.19 \[ -\frac{1}{6 \,{\left (b x^{3} + a\right )}^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(b*x^3 + a)^3,x, algorithm="giac")
[Out]