Optimal. Leaf size=21 \[ \log (x) x^{-n p q} \left (a \left (b x^n\right )^p\right )^q \]
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Rubi [A] time = 0.0757675, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.095 \[ \log (x) x^{-n p q} \left (a \left (b x^n\right )^p\right )^q \]
Antiderivative was successfully verified.
[In] Int[x^(-1 - n*p*q)*(a*(b*x^n)^p)^q,x]
[Out]
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Rubi in Sympy [A] time = 8.69296, size = 19, normalized size = 0.9 \[ x^{- n p q} \left (a \left (b x^{n}\right )^{p}\right )^{q} \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(-n*p*q-1)*(a*(b*x**n)**p)**q,x)
[Out]
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Mathematica [A] time = 0.0114324, size = 21, normalized size = 1. \[ \log (x) x^{-n p q} \left (a \left (b x^n\right )^p\right )^q \]
Antiderivative was successfully verified.
[In] Integrate[x^(-1 - n*p*q)*(a*(b*x^n)^p)^q,x]
[Out]
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Maple [F] time = 0.252, size = 0, normalized size = 0. \[ \int{x}^{-npq-1} \left ( a \left ( b{x}^{n} \right ) ^{p} \right ) ^{q}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(-n*p*q-1)*(a*(b*x^n)^p)^q,x)
[Out]
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Maxima [A] time = 1.83342, size = 15, normalized size = 0.71 \[ a^{q}{\left (b^{p}\right )}^{q} \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(((b*x^n)^p*a)^q*x^(-n*p*q - 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.233747, size = 19, normalized size = 0.9 \[ e^{\left (p q \log \left (b\right ) + q \log \left (a\right )\right )} \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(((b*x^n)^p*a)^q*x^(-n*p*q - 1),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(-n*p*q-1)*(a*(b*x**n)**p)**q,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \left (\left (b x^{n}\right )^{p} a\right )^{q} x^{-n p q - 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(((b*x^n)^p*a)^q*x^(-n*p*q - 1),x, algorithm="giac")
[Out]