Optimal. Leaf size=14 \[ \frac{3 x}{5 \sqrt [3]{\frac{b}{x^2}}} \]
[Out]
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Rubi [A] time = 0.00650845, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ \frac{3 x}{5 \sqrt [3]{\frac{b}{x^2}}} \]
Antiderivative was successfully verified.
[In] Int[(b/x^2)^(-1/3),x]
[Out]
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Rubi in Sympy [A] time = 1.53033, size = 15, normalized size = 1.07 \[ \frac{3 x^{3} \left (\frac{b}{x^{2}}\right )^{\frac{2}{3}}}{5 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b/x**2)**(1/3),x)
[Out]
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Mathematica [A] time = 0.00333646, size = 14, normalized size = 1. \[ \frac{3 x}{5 \sqrt [3]{\frac{b}{x^2}}} \]
Antiderivative was successfully verified.
[In] Integrate[(b/x^2)^(-1/3),x]
[Out]
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Maple [A] time = 0.003, size = 11, normalized size = 0.8 \[{\frac{3\,x}{5}{\frac{1}{\sqrt [3]{{\frac{b}{{x}^{2}}}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b/x^2)^(1/3),x)
[Out]
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Maxima [A] time = 1.43944, size = 14, normalized size = 1. \[ \frac{3 \, x}{5 \, \left (\frac{b}{x^{2}}\right )^{\frac{1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b/x^2)^(-1/3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.21559, size = 20, normalized size = 1.43 \[ \frac{3 \, x^{3} \left (\frac{b}{x^{2}}\right )^{\frac{2}{3}}}{5 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b/x^2)^(-1/3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.54498, size = 17, normalized size = 1.21 \[ \frac{3 x}{5 \sqrt [3]{b} \sqrt [3]{\frac{1}{x^{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b/x**2)**(1/3),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\left (\frac{b}{x^{2}}\right )^{\frac{1}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b/x^2)^(-1/3),x, algorithm="giac")
[Out]