Optimal. Leaf size=12 \[ -\frac{3 x}{\sqrt [3]{b x^4}} \]
[Out]
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Rubi [A] time = 0.00715354, antiderivative size = 12, 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 \[ -\frac{3 x}{\sqrt [3]{b x^4}} \]
Antiderivative was successfully verified.
[In] Int[(b*x^4)^(-1/3),x]
[Out]
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Rubi in Sympy [A] time = 1.58078, size = 15, normalized size = 1.25 \[ - \frac{3 \left (b x^{4}\right )^{\frac{2}{3}}}{b x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*x**4)**(1/3),x)
[Out]
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Mathematica [A] time = 0.00360877, size = 12, normalized size = 1. \[ -\frac{3 x}{\sqrt [3]{b x^4}} \]
Antiderivative was successfully verified.
[In] Integrate[(b*x^4)^(-1/3),x]
[Out]
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Maple [A] time = 0.001, size = 11, normalized size = 0.9 \[ -3\,{\frac{x}{\sqrt [3]{b{x}^{4}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b*x^4)^(1/3),x)
[Out]
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Maxima [A] time = 1.44035, size = 14, normalized size = 1.17 \[ -\frac{3 \, x}{\left (b x^{4}\right )^{\frac{1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4)^(-1/3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.21686, size = 20, normalized size = 1.67 \[ -\frac{3 \, \left (b x^{4}\right )^{\frac{2}{3}}}{b x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4)^(-1/3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.52865, size = 15, normalized size = 1.25 \[ - \frac{3 x}{\sqrt [3]{b} \sqrt [3]{x^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*x**4)**(1/3),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\left (b x^{4}\right )^{\frac{1}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4)^(-1/3),x, algorithm="giac")
[Out]