Optimal. Leaf size=16 \[ \log (x) x^{-n p} \left (a x^n\right )^p \]
[Out]
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Rubi [A] time = 0.00998475, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ \log (x) x^{-n p} \left (a x^n\right )^p \]
Antiderivative was successfully verified.
[In] Int[x^(-1 - n*p)*(a*x^n)^p,x]
[Out]
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Rubi in Sympy [A] time = 2.36821, size = 14, normalized size = 0.88 \[ x^{- n p} \left (a x^{n}\right )^{p} \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(-n*p-1)*(a*x**n)**p,x)
[Out]
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Mathematica [A] time = 0.0082386, size = 16, normalized size = 1. \[ \log (x) x^{-n p} \left (a x^n\right )^p \]
Antiderivative was successfully verified.
[In] Integrate[x^(-1 - n*p)*(a*x^n)^p,x]
[Out]
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Maple [F] time = 0.061, size = 0, normalized size = 0. \[ \int{x}^{-np-1} \left ( a{x}^{n} \right ) ^{p}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(-n*p-1)*(a*x^n)^p,x)
[Out]
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Maxima [A] time = 1.50487, size = 8, normalized size = 0.5 \[ a^{p} \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a*x^n)^p*x^(-n*p - 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.226825, size = 8, normalized size = 0.5 \[ a^{p} \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a*x^n)^p*x^(-n*p - 1),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int x^{- n p - 1} \left (a x^{n}\right )^{p}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(-n*p-1)*(a*x**n)**p,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \left (a x^{n}\right )^{p} x^{-n p - 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a*x^n)^p*x^(-n*p - 1),x, algorithm="giac")
[Out]