Optimal. Leaf size=22 \[ x^{m+1} \log (x) \left (a x^n\right )^{-\frac{m+1}{n}} \]
[Out]
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Rubi [A] time = 0.0118048, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ x^{m+1} \log (x) \left (a x^n\right )^{-\frac{m+1}{n}} \]
Antiderivative was successfully verified.
[In] Int[x^m/(a*x^n)^((1 + m)/n),x]
[Out]
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Rubi in Sympy [A] time = 2.81269, size = 17, normalized size = 0.77 \[ x^{m + 1} \left (a x^{n}\right )^{- \frac{m + 1}{n}} \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**m/((a*x**n)**((1+m)/n)),x)
[Out]
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Mathematica [A] time = 0.0148402, size = 22, normalized size = 1. \[ x^{m+1} \log (x) \left (a x^n\right )^{-\frac{m+1}{n}} \]
Antiderivative was successfully verified.
[In] Integrate[x^m/(a*x^n)^((1 + m)/n),x]
[Out]
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Maple [F] time = 0.069, size = 0, normalized size = 0. \[ \int{{x}^{m} \left ( \left ( a{x}^{n} \right ) ^{{\frac{1+m}{n}}} \right ) ^{-1}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^m/((a*x^n)^((1+m)/n)),x)
[Out]
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Maxima [A] time = 1.51359, size = 23, normalized size = 1.05 \[ a^{-\frac{m}{n} - \frac{1}{n}} \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^m/(a*x^n)^((m + 1)/n),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.238728, size = 19, normalized size = 0.86 \[ \frac{\log \left (x\right )}{a^{\frac{m + 1}{n}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^m/(a*x^n)^((m + 1)/n),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int x^{m} \left (a x^{n}\right )^{- \frac{m + 1}{n}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**m/((a*x**n)**((1+m)/n)),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{m}}{\left (a x^{n}\right )^{\frac{m + 1}{n}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^m/(a*x^n)^((m + 1)/n),x, algorithm="giac")
[Out]