Optimal. Leaf size=13 \[ x^{-2 p} \left (x^2\right )^p \log (x) \]
[Out]
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Rubi [A] time = 0.00830932, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ x^{-2 p} \left (x^2\right )^p \log (x) \]
Antiderivative was successfully verified.
[In] Int[x^(-1 - 2*p)*(x^2)^p,x]
[Out]
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Rubi in Sympy [A] time = 1.93873, size = 12, normalized size = 0.92 \[ x^{- 2 p} \left (x^{2}\right )^{p} \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(-1-2*p)*(x**2)**p,x)
[Out]
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Mathematica [A] time = 0.00957261, size = 13, normalized size = 1. \[ x^{-2 p} \left (x^2\right )^p \log (x) \]
Antiderivative was successfully verified.
[In] Integrate[x^(-1 - 2*p)*(x^2)^p,x]
[Out]
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Maple [A] time = 0.035, size = 21, normalized size = 1.6 \[ x\ln \left ( x \right ){{\rm e}^{p\ln \left ({x}^{2} \right ) }}{{\rm e}^{ \left ( -1-2\,p \right ) \ln \left ( x \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(-1-2*p)*(x^2)^p,x)
[Out]
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Maxima [A] time = 1.44193, size = 3, normalized size = 0.23 \[ \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2)^p*x^(-2*p - 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.260038, size = 3, normalized size = 0.23 \[ \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2)^p*x^(-2*p - 1),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int x^{- 2 p - 1} \left (x^{2}\right )^{p}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(-1-2*p)*(x**2)**p,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (x^{2}\right )}^{p} x^{-2 \, p - 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2)^p*x^(-2*p - 1),x, algorithm="giac")
[Out]