Optimal. Leaf size=17 \[ -\log (3-x)+\log (x)+2 \log (x+3) \]
[Out]
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Rubi [A] time = 0.0526702, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ -\log (3-x)+\log (x)+2 \log (x+3) \]
Antiderivative was successfully verified.
[In] Int[(-9 - 9*x + 2*x^2)/(-9*x + x^3),x]
[Out]
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Rubi in Sympy [A] time = 9.1575, size = 14, normalized size = 0.82 \[ \log{\left (x \right )} - \log{\left (- x + 3 \right )} + 2 \log{\left (x + 3 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2*x**2-9*x-9)/(x**3-9*x),x)
[Out]
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Mathematica [A] time = 0.00906288, size = 17, normalized size = 1. \[ -\log (3-x)+\log (x)+2 \log (x+3) \]
Antiderivative was successfully verified.
[In] Integrate[(-9 - 9*x + 2*x^2)/(-9*x + x^3),x]
[Out]
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Maple [A] time = 0.011, size = 16, normalized size = 0.9 \[ -\ln \left ( -3+x \right ) +\ln \left ( x \right ) +2\,\ln \left ( 3+x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2*x^2-9*x-9)/(x^3-9*x),x)
[Out]
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Maxima [A] time = 0.996735, size = 20, normalized size = 1.18 \[ 2 \, \log \left (x + 3\right ) - \log \left (x - 3\right ) + \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x^2 - 9*x - 9)/(x^3 - 9*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.258079, size = 20, normalized size = 1.18 \[ 2 \, \log \left (x + 3\right ) - \log \left (x - 3\right ) + \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x^2 - 9*x - 9)/(x^3 - 9*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.270863, size = 14, normalized size = 0.82 \[ \log{\left (x \right )} - \log{\left (x - 3 \right )} + 2 \log{\left (x + 3 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x**2-9*x-9)/(x**3-9*x),x)
[Out]
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GIAC/XCAS [A] time = 0.262644, size = 24, normalized size = 1.41 \[ 2 \,{\rm ln}\left ({\left | x + 3 \right |}\right ) -{\rm ln}\left ({\left | x - 3 \right |}\right ) +{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x^2 - 9*x - 9)/(x^3 - 9*x),x, algorithm="giac")
[Out]