Optimal. Leaf size=13 \[ \frac{x \log (x)}{\sqrt [3]{b x^3}} \]
[Out]
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Rubi [A] time = 0.00639038, antiderivative size = 13, 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 \[ \frac{x \log (x)}{\sqrt [3]{b x^3}} \]
Antiderivative was successfully verified.
[In] Int[(b*x^3)^(-1/3),x]
[Out]
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Rubi in Sympy [A] time = 1.55394, size = 15, normalized size = 1.15 \[ \frac{\left (b x^{3}\right )^{\frac{2}{3}} \log{\left (x \right )}}{b x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*x**3)**(1/3),x)
[Out]
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Mathematica [A] time = 0.00315503, size = 13, normalized size = 1. \[ \frac{x \log (x)}{\sqrt [3]{b x^3}} \]
Antiderivative was successfully verified.
[In] Integrate[(b*x^3)^(-1/3),x]
[Out]
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Maple [A] time = 0.013, size = 12, normalized size = 0.9 \[{x\ln \left ( x \right ){\frac{1}{\sqrt [3]{b{x}^{3}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b*x^3)^(1/3),x)
[Out]
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Maxima [A] time = 1.43088, size = 15, normalized size = 1.15 \[ \frac{x \log \left (x\right )}{\left (b x^{3}\right )^{\frac{1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3)^(-1/3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.226334, size = 22, normalized size = 1.69 \[ \frac{\left (b x^{3}\right )^{\frac{2}{3}} \log \left (x\right )}{b x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3)^(-1/3),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt [3]{b x^{3}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*x**3)**(1/3),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\left (b x^{3}\right )^{\frac{1}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3)^(-1/3),x, algorithm="giac")
[Out]