Optimal. Leaf size=19 \[ -\frac{\sqrt [3]{a+b x^3}}{a x} \]
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Rubi [A] time = 0.0200223, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ -\frac{\sqrt [3]{a+b x^3}}{a x} \]
Antiderivative was successfully verified.
[In] Int[1/(x^2*(a + b*x^3)^(2/3)),x]
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Rubi in Sympy [A] time = 2.67965, size = 14, normalized size = 0.74 \[ - \frac{\sqrt [3]{a + b x^{3}}}{a x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**2/(b*x**3+a)**(2/3),x)
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Mathematica [A] time = 0.0147874, size = 19, normalized size = 1. \[ -\frac{\sqrt [3]{a+b x^3}}{a x} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^2*(a + b*x^3)^(2/3)),x]
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Maple [A] time = 0.004, size = 18, normalized size = 1. \[ -{\frac{1}{ax}\sqrt [3]{b{x}^{3}+a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^2/(b*x^3+a)^(2/3),x)
[Out]
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Maxima [A] time = 1.44057, size = 23, normalized size = 1.21 \[ -\frac{{\left (b x^{3} + a\right )}^{\frac{1}{3}}}{a x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^3 + a)^(2/3)*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.234428, size = 23, normalized size = 1.21 \[ -\frac{{\left (b x^{3} + a\right )}^{\frac{1}{3}}}{a x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^3 + a)^(2/3)*x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.21171, size = 31, normalized size = 1.63 \[ \frac{\sqrt [3]{b} \sqrt [3]{\frac{a}{b x^{3}} + 1} \Gamma \left (- \frac{1}{3}\right )}{3 a \Gamma \left (\frac{2}{3}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**2/(b*x**3+a)**(2/3),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x^{3} + a\right )}^{\frac{2}{3}} x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^3 + a)^(2/3)*x^2),x, algorithm="giac")
[Out]