Optimal. Leaf size=18 \[ x-\log (1-x)+4 \log (2-x) \]
[Out]
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Rubi [A] time = 0.0308976, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.214 \[ x-\log (1-x)+4 \log (2-x) \]
Antiderivative was successfully verified.
[In] Int[x^2/(2 - 3*x + x^2),x]
[Out]
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Rubi in Sympy [A] time = 6.55147, size = 12, normalized size = 0.67 \[ x - \log{\left (- x + 1 \right )} + 4 \log{\left (- x + 2 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/(x**2-3*x+2),x)
[Out]
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Mathematica [A] time = 0.00679068, size = 18, normalized size = 1. \[ x-\log (1-x)+4 \log (2-x) \]
Antiderivative was successfully verified.
[In] Integrate[x^2/(2 - 3*x + x^2),x]
[Out]
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Maple [A] time = 0.008, size = 15, normalized size = 0.8 \[ x-\ln \left ( -1+x \right ) +4\,\ln \left ( x-2 \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/(x^2-3*x+2),x)
[Out]
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Maxima [A] time = 0.669705, size = 19, normalized size = 1.06 \[ x - \log \left (x - 1\right ) + 4 \, \log \left (x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(x^2 - 3*x + 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.201707, size = 19, normalized size = 1.06 \[ x - \log \left (x - 1\right ) + 4 \, \log \left (x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(x^2 - 3*x + 2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.197611, size = 12, normalized size = 0.67 \[ x + 4 \log{\left (x - 2 \right )} - \log{\left (x - 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2/(x**2-3*x+2),x)
[Out]
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GIAC/XCAS [A] time = 0.203858, size = 22, normalized size = 1.22 \[ x -{\rm ln}\left ({\left | x - 1 \right |}\right ) + 4 \,{\rm ln}\left ({\left | x - 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(x^2 - 3*x + 2),x, algorithm="giac")
[Out]