Optimal. Leaf size=26 \[ \frac{x^2}{2}+2 x+\frac{1}{1-x}+3 \log (1-x) \]
[Out]
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Rubi [A] time = 0.0291117, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ \frac{x^2}{2}+2 x+\frac{1}{1-x}+3 \log (1-x) \]
Antiderivative was successfully verified.
[In] Int[x^3/(1 - 2*x + x^2),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ 3 \log{\left (- x + 1 \right )} + 4 \int \frac{1}{2}\, dx + \int x\, dx + \frac{1}{- x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3/(x**2-2*x+1),x)
[Out]
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Mathematica [A] time = 0.0143132, size = 25, normalized size = 0.96 \[ \frac{1}{2} \left (x^2+4 x-\frac{2}{x-1}+6 \log (x-1)-5\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^3/(1 - 2*x + x^2),x]
[Out]
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Maple [A] time = 0.008, size = 23, normalized size = 0.9 \[ 2\,x+{\frac{{x}^{2}}{2}}+3\,\ln \left ( -1+x \right ) - \left ( -1+x \right ) ^{-1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3/(x^2-2*x+1),x)
[Out]
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Maxima [A] time = 0.673086, size = 30, normalized size = 1.15 \[ \frac{1}{2} \, x^{2} + 2 \, x - \frac{1}{x - 1} + 3 \, \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(x^2 - 2*x + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.201684, size = 39, normalized size = 1.5 \[ \frac{x^{3} + 3 \, x^{2} + 6 \,{\left (x - 1\right )} \log \left (x - 1\right ) - 4 \, x - 2}{2 \,{\left (x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(x^2 - 2*x + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.137438, size = 19, normalized size = 0.73 \[ \frac{x^{2}}{2} + 2 x + 3 \log{\left (x - 1 \right )} - \frac{1}{x - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3/(x**2-2*x+1),x)
[Out]
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GIAC/XCAS [A] time = 0.204206, size = 31, normalized size = 1.19 \[ \frac{1}{2} \, x^{2} + 2 \, x - \frac{1}{x - 1} + 3 \,{\rm ln}\left ({\left | x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(x^2 - 2*x + 1),x, algorithm="giac")
[Out]