Optimal. Leaf size=23 \[ -\frac{\sqrt [3]{a x^3+b x^6}}{a x^2} \]
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Rubi [A] time = 0.0130483, antiderivative size = 23, 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 \[ -\frac{\sqrt [3]{a x^3+b x^6}}{a x^2} \]
Antiderivative was successfully verified.
[In] Int[(a*x^3 + b*x^6)^(-2/3),x]
[Out]
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Rubi in Sympy [A] time = 1.38468, size = 19, normalized size = 0.83 \[ - \frac{\sqrt [3]{a x^{3} + b x^{6}}}{a x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*x**6+a*x**3)**(2/3),x)
[Out]
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Mathematica [A] time = 0.0216424, size = 23, normalized size = 1. \[ -\frac{\sqrt [3]{x^3 \left (a+b x^3\right )}}{a x^2} \]
Antiderivative was successfully verified.
[In] Integrate[(a*x^3 + b*x^6)^(-2/3),x]
[Out]
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Maple [A] time = 0.006, size = 27, normalized size = 1.2 \[ -{\frac{x \left ( b{x}^{3}+a \right ) }{a} \left ( b{x}^{6}+a{x}^{3} \right ) ^{-{\frac{2}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b*x^6+a*x^3)^(2/3),x)
[Out]
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Maxima [A] time = 0.767714, size = 23, normalized size = 1. \[ -\frac{{\left (b x^{3} + a\right )}^{\frac{1}{3}}}{a x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^6 + a*x^3)^(-2/3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.274283, size = 28, normalized size = 1.22 \[ -\frac{{\left (b x^{6} + a x^{3}\right )}^{\frac{1}{3}}}{a x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^6 + a*x^3)^(-2/3),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\left (a x^{3} + b x^{6}\right )^{\frac{2}{3}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*x**6+a*x**3)**(2/3),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x^{6} + a x^{3}\right )}^{\frac{2}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^6 + a*x^3)^(-2/3),x, algorithm="giac")
[Out]