Optimal. Leaf size=14 \[ \frac{3 x}{4 \sqrt [3]{\frac{b}{x}}} \]
[Out]
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Rubi [A] time = 0.00652189, 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 \[ \frac{3 x}{4 \sqrt [3]{\frac{b}{x}}} \]
Antiderivative was successfully verified.
[In] Int[(b/x)^(-1/3),x]
[Out]
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Rubi in Sympy [A] time = 1.55098, size = 14, normalized size = 1. \[ \frac{3 x^{2} \left (\frac{b}{x}\right )^{\frac{2}{3}}}{4 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b/x)**(1/3),x)
[Out]
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Mathematica [A] time = 0.00291345, size = 14, normalized size = 1. \[ \frac{3 x}{4 \sqrt [3]{\frac{b}{x}}} \]
Antiderivative was successfully verified.
[In] Integrate[(b/x)^(-1/3),x]
[Out]
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Maple [A] time = 0.003, size = 11, normalized size = 0.8 \[{\frac{3\,x}{4}{\frac{1}{\sqrt [3]{{\frac{b}{x}}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b/x)^(1/3),x)
[Out]
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Maxima [A] time = 1.4399, size = 14, normalized size = 1. \[ \frac{3 \, x}{4 \, \left (\frac{b}{x}\right )^{\frac{1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b/x)^(-1/3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.216844, size = 14, normalized size = 1. \[ \frac{3 \, x}{4 \, \left (\frac{b}{x}\right )^{\frac{1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b/x)^(-1/3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.56895, size = 15, normalized size = 1.07 \[ \frac{3 x}{4 \sqrt [3]{b} \sqrt [3]{\frac{1}{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b/x)**(1/3),x)
[Out]
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GIAC/XCAS [A] time = 0.228809, size = 14, normalized size = 1. \[ \frac{3 \, x}{4 \, \left (\frac{b}{x}\right )^{\frac{1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b/x)^(-1/3),x, algorithm="giac")
[Out]