Optimal. Leaf size=27 \[ \frac{x^2}{2}+3 x-\log (1-x)+8 \log (2-x) \]
[Out]
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Rubi [A] time = 0.0392936, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 3, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.214 \[ \frac{x^2}{2}+3 x-\log (1-x)+8 \log (2-x) \]
Antiderivative was successfully verified.
[In] Int[x^3/(2 - 3*x + x^2),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ 3 x - \log{\left (- x + 1 \right )} + 8 \log{\left (- x + 2 \right )} + \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3/(x**2-3*x+2),x)
[Out]
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Mathematica [A] time = 0.00688475, size = 27, normalized size = 1. \[ \frac{x^2}{2}+3 x-\log (1-x)+8 \log (2-x) \]
Antiderivative was successfully verified.
[In] Integrate[x^3/(2 - 3*x + x^2),x]
[Out]
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Maple [A] time = 0.007, size = 22, normalized size = 0.8 \[ 3\,x+{\frac{{x}^{2}}{2}}-\ln \left ( -1+x \right ) +8\,\ln \left ( x-2 \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3/(x^2-3*x+2),x)
[Out]
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Maxima [A] time = 0.677108, size = 28, normalized size = 1.04 \[ \frac{1}{2} \, x^{2} + 3 \, x - \log \left (x - 1\right ) + 8 \, \log \left (x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(x^2 - 3*x + 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.201441, size = 28, normalized size = 1.04 \[ \frac{1}{2} \, x^{2} + 3 \, x - \log \left (x - 1\right ) + 8 \, \log \left (x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(x^2 - 3*x + 2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.196264, size = 19, normalized size = 0.7 \[ \frac{x^{2}}{2} + 3 x + 8 \log{\left (x - 2 \right )} - \log{\left (x - 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3/(x**2-3*x+2),x)
[Out]
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GIAC/XCAS [A] time = 0.204488, size = 31, normalized size = 1.15 \[ \frac{1}{2} \, x^{2} + 3 \, x -{\rm ln}\left ({\left | x - 1 \right |}\right ) + 8 \,{\rm ln}\left ({\left | x - 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(x^2 - 3*x + 2),x, algorithm="giac")
[Out]