Optimal. Leaf size=12 \[ \frac{1}{x}+3 \log (1-x) \]
[Out]
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Rubi [A] time = 0.0433017, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{1}{x}+3 \log (1-x) \]
Antiderivative was successfully verified.
[In] Int[(1 - x + 3*x^2)/(-x^2 + x^3),x]
[Out]
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Rubi in Sympy [A] time = 7.00016, size = 8, normalized size = 0.67 \[ 3 \log{\left (- x + 1 \right )} + \frac{1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3*x**2-x+1)/(x**3-x**2),x)
[Out]
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Mathematica [A] time = 0.00578145, size = 12, normalized size = 1. \[ \frac{1}{x}+3 \log (1-x) \]
Antiderivative was successfully verified.
[In] Integrate[(1 - x + 3*x^2)/(-x^2 + x^3),x]
[Out]
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Maple [A] time = 0.007, size = 11, normalized size = 0.9 \[ 3\,\ln \left ( -1+x \right ) +{x}^{-1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3*x^2-x+1)/(x^3-x^2),x)
[Out]
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Maxima [A] time = 0.812893, size = 14, normalized size = 1.17 \[ \frac{1}{x} + 3 \, \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x^2 - x + 1)/(x^3 - x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.249535, size = 18, normalized size = 1.5 \[ \frac{3 \, x \log \left (x - 1\right ) + 1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x^2 - x + 1)/(x^3 - x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.169184, size = 8, normalized size = 0.67 \[ 3 \log{\left (x - 1 \right )} + \frac{1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x**2-x+1)/(x**3-x**2),x)
[Out]
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GIAC/XCAS [A] time = 0.262483, size = 15, normalized size = 1.25 \[ \frac{1}{x} + 3 \,{\rm ln}\left ({\left | x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x^2 - x + 1)/(x^3 - x^2),x, algorithm="giac")
[Out]