Optimal. Leaf size=19 \[ \frac{3 x}{(3-n) \sqrt [3]{b x^n}} \]
[Out]
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Rubi [A] time = 0.0142028, antiderivative size = 19, 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 \[ \frac{3 x}{(3-n) \sqrt [3]{b x^n}} \]
Antiderivative was successfully verified.
[In] Int[(b*x^n)^(-1/3),x]
[Out]
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Rubi in Sympy [A] time = 2.83268, size = 27, normalized size = 1.42 \[ \frac{3 x^{- \frac{2 n}{3}} x^{- \frac{n}{3} + 1} \left (b x^{n}\right )^{\frac{2}{3}}}{b \left (- n + 3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*x**n)**(1/3),x)
[Out]
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Mathematica [A] time = 0.0082226, size = 17, normalized size = 0.89 \[ -\frac{3 x}{(n-3) \sqrt [3]{b x^n}} \]
Antiderivative was successfully verified.
[In] Integrate[(b*x^n)^(-1/3),x]
[Out]
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Maple [A] time = 0.002, size = 16, normalized size = 0.8 \[ -3\,{\frac{x}{ \left ( -3+n \right ) \sqrt [3]{b{x}^{n}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b*x^n)^(1/3),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n)^(-1/3),x, algorithm="maxima")
[Out]
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Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n)^(-1/3),x, algorithm="fricas")
[Out]
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Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*x**n)**(1/3),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\left (b x^{n}\right )^{\frac{1}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n)^(-1/3),x, algorithm="giac")
[Out]