Optimal. Leaf size=25 \[ \frac{1}{2} x^3 \left (a \left (b x^m\right )^n\right )^{-\frac{1}{m n}} \]
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Rubi [A] time = 0.085973, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{1}{2} x^3 \left (a \left (b x^m\right )^n\right )^{-\frac{1}{m n}} \]
Antiderivative was successfully verified.
[In] Int[x^2/(a*(b*x^m)^n)^(1/(m*n)),x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ x \left (a \left (b x^{m}\right )^{n}\right )^{- \frac{1}{m n}} \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/((a*(b*x**m)**n)**(1/m/n)),x)
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Mathematica [A] time = 0.0175664, size = 25, normalized size = 1. \[ \frac{1}{2} x^3 \left (a \left (b x^m\right )^n\right )^{-\frac{1}{m n}} \]
Antiderivative was successfully verified.
[In] Integrate[x^2/(a*(b*x^m)^n)^(1/(m*n)),x]
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Maple [A] time = 0.003, size = 25, normalized size = 1. \[{\frac{{x}^{3}}{2} \left ( \left ( a \left ( b{x}^{m} \right ) ^{n} \right ) ^{{\frac{1}{mn}}} \right ) ^{-1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/((a*(b*x^m)^n)^(1/m/n)),x)
[Out]
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Maxima [A] time = 1.71287, size = 55, normalized size = 2.2 \[ \frac{1}{2} \, a^{-\frac{1}{m n}}{\left (b^{n}\right )}^{-\frac{1}{m n}} x^{3}{\left ({\left (x^{m}\right )}^{n}\right )}^{-\frac{1}{m n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/((b*x^m)^n*a)^(1/(m*n)),x, algorithm="maxima")
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Fricas [A] time = 0.236403, size = 28, normalized size = 1.12 \[ \frac{1}{2} \, x^{2} e^{\left (-\frac{n \log \left (b\right ) + \log \left (a\right )}{m n}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/((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**2/((a*(b*x**m)**n)**(1/m/n)),x)
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GIAC/XCAS [A] time = 0.276686, size = 28, normalized size = 1.12 \[ \frac{1}{2} \, x^{2} e^{\left (-\frac{n{\rm ln}\left (b\right ) +{\rm ln}\left (a\right )}{m n}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/((b*x^m)^n*a)^(1/(m*n)),x, algorithm="giac")
[Out]