Optimal. Leaf size=13 \[ -\left (a x^n\right )^{-1/n} \]
[Out]
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Rubi [A] time = 0.00704155, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\left (a x^n\right )^{-1/n} \]
Antiderivative was successfully verified.
[In] Int[1/(x*(a*x^n)^n^(-1)),x]
[Out]
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Rubi in Sympy [A] time = 3.00404, size = 10, normalized size = 0.77 \[ - \left (a x^{n}\right )^{- \frac{1}{n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/((a*x**n)**(1/n)),x)
[Out]
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Mathematica [A] time = 0.00242291, size = 13, normalized size = 1. \[ -\left (a x^n\right )^{-1/n} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x*(a*x^n)^n^(-1)),x]
[Out]
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Maple [A] time = 0.003, size = 14, normalized size = 1.1 \[ - \left ( \sqrt [n]{a{x}^{n}} \right ) ^{-1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/((a*x^n)^(1/n)),x)
[Out]
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Maxima [A] time = 1.45968, size = 24, normalized size = 1.85 \[ -a^{-\frac{1}{n}}{\left (x^{n}\right )}^{-\frac{1}{n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a*x^n)^(1/n)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.225973, size = 16, normalized size = 1.23 \[ -\frac{1}{a^{\left (\frac{1}{n}\right )} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a*x^n)^(1/n)*x),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(1/x/((a*x**n)**(1/n)),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\left (a x^{n}\right )^{\left (\frac{1}{n}\right )} x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a*x^n)^(1/n)*x),x, algorithm="giac")
[Out]