Optimal. Leaf size=22 \[ x^2 \left (a \left (b x^m\right )^n\right )^{-\frac{1}{m n}} \]
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Rubi [A] time = 0.0534592, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ x^2 \left (a \left (b x^m\right )^n\right )^{-\frac{1}{m n}} \]
Antiderivative was successfully verified.
[In] Int[x/(a*(b*x^m)^n)^(1/(m*n)),x]
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Rubi in Sympy [A] time = 4.87992, size = 15, normalized size = 0.68 \[ x^{2} \left (a \left (b x^{m}\right )^{n}\right )^{- \frac{1}{m n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/((a*(b*x**m)**n)**(1/m/n)),x)
[Out]
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Mathematica [A] time = 0.00506245, size = 22, normalized size = 1. \[ x^2 \left (a \left (b x^m\right )^n\right )^{-\frac{1}{m n}} \]
Antiderivative was successfully verified.
[In] Integrate[x/(a*(b*x^m)^n)^(1/(m*n)),x]
[Out]
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Maple [F] time = 0.156, size = 0, normalized size = 0. \[ \int{x \left ( \left ( a \left ( b{x}^{m} \right ) ^{n} \right ) ^{{\frac{1}{mn}}} \right ) ^{-1}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/((a*(b*x^m)^n)^(1/m/n)),x)
[Out]
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Maxima [A] time = 1.70536, size = 54, normalized size = 2.45 \[ a^{-\frac{1}{m n}}{\left (b^{n}\right )}^{-\frac{1}{m n}} x^{2}{\left ({\left (x^{m}\right )}^{n}\right )}^{-\frac{1}{m n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/((b*x^m)^n*a)^(1/(m*n)),x, algorithm="maxima")
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Fricas [A] time = 0.231631, size = 24, normalized size = 1.09 \[ x e^{\left (-\frac{n \log \left (b\right ) + \log \left (a\right )}{m n}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/((b*x^m)^n*a)^(1/(m*n)),x, algorithm="fricas")
[Out]
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Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: RecursionError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/((a*(b*x**m)**n)**(1/m/n)),x)
[Out]
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GIAC/XCAS [A] time = 0.265597, size = 24, normalized size = 1.09 \[ x e^{\left (-\frac{n{\rm ln}\left (b\right ) +{\rm ln}\left (a\right )}{m n}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/((b*x^m)^n*a)^(1/(m*n)),x, algorithm="giac")
[Out]