Optimal. Leaf size=19 \[ \log (1-x)-2 \log (x+2)-3 \log (x+3) \]
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Rubi [A] time = 0.0477299, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042 \[ \log (1-x)-2 \log (x+2)-3 \log (x+3) \]
Antiderivative was successfully verified.
[In] Int[(18 - 2*x - 4*x^2)/(-6 + x + 4*x^2 + x^3),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{- 4 x^{2} - 2 x + 18}{x^{3} + 4 x^{2} + x - 6}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-4*x**2-2*x+18)/(x**3+4*x**2+x-6),x)
[Out]
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Mathematica [A] time = 0.0108794, size = 25, normalized size = 1.32 \[ -2 \left (-\frac{1}{2} \log (1-x)+\log (x+2)+\frac{3}{2} \log (x+3)\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(18 - 2*x - 4*x^2)/(-6 + x + 4*x^2 + x^3),x]
[Out]
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Maple [A] time = 0.012, size = 18, normalized size = 1. \[ -2\,\ln \left ( 2+x \right ) +\ln \left ( -1+x \right ) -3\,\ln \left ( 3+x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-4*x^2-2*x+18)/(x^3+4*x^2+x-6),x)
[Out]
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Maxima [A] time = 1.35688, size = 23, normalized size = 1.21 \[ -3 \, \log \left (x + 3\right ) - 2 \, \log \left (x + 2\right ) + \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-2*(2*x^2 + x - 9)/(x^3 + 4*x^2 + x - 6),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217169, size = 23, normalized size = 1.21 \[ -3 \, \log \left (x + 3\right ) - 2 \, \log \left (x + 2\right ) + \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-2*(2*x^2 + x - 9)/(x^3 + 4*x^2 + x - 6),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.138196, size = 17, normalized size = 0.89 \[ \log{\left (x - 1 \right )} - 2 \log{\left (x + 2 \right )} - 3 \log{\left (x + 3 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-4*x**2-2*x+18)/(x**3+4*x**2+x-6),x)
[Out]
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GIAC/XCAS [A] time = 0.203251, size = 27, normalized size = 1.42 \[ -3 \,{\rm ln}\left ({\left | x + 3 \right |}\right ) - 2 \,{\rm ln}\left ({\left | x + 2 \right |}\right ) +{\rm ln}\left ({\left | x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-2*(2*x^2 + x - 9)/(x^3 + 4*x^2 + x - 6),x, algorithm="giac")
[Out]