Optimal. Leaf size=15 \[ x \log (x) \left (a x^n\right )^{-1/n} \]
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Rubi [A] time = 0.00702907, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ x \log (x) \left (a x^n\right )^{-1/n} \]
Antiderivative was successfully verified.
[In] Int[(a*x^n)^(-n^(-1)),x]
[Out]
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Rubi in Sympy [A] time = 1.35889, size = 12, normalized size = 0.8 \[ x \left (a x^{n}\right )^{- \frac{1}{n}} \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/((a*x**n)**(1/n)),x)
[Out]
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Mathematica [A] time = 0.00207765, size = 15, normalized size = 1. \[ x \log (x) \left (a x^n\right )^{-1/n} \]
Antiderivative was successfully verified.
[In] Integrate[(a*x^n)^(-n^(-1)),x]
[Out]
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Maple [A] time = 0.029, size = 29, normalized size = 1.9 \[{\frac{x\ln \left ( a{{\rm e}^{n\ln \left ( x \right ) }} \right ) }{n} \left ({{\rm e}^{{\frac{\ln \left ( a{{\rm e}^{n\ln \left ( x \right ) }} \right ) }{n}}}} \right ) ^{-1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/((a*x^n)^(1/n)),x)
[Out]
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Maxima [A] time = 1.57134, size = 14, normalized size = 0.93 \[ a^{-\frac{1}{n}} \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a*x^n)^(1/n)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.231388, size = 14, normalized size = 0.93 \[ \frac{\log \left (x\right )}{a^{\left (\frac{1}{n}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a*x^n)^(1/n)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \left (a x^{n}\right )^{- \frac{1}{n}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a*x**n)**(1/n)),x)
[Out]
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GIAC/XCAS [A] time = 0.232602, size = 15, normalized size = 1. \[ e^{\left (-\frac{{\rm ln}\left (a\right )}{n}\right )}{\rm ln}\left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a*x^n)^(1/n)),x, algorithm="giac")
[Out]