Optimal. Leaf size=22 \[ \frac{x^3}{3}+x^2+4 x+9 \log (2-x) \]
[Out]
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Rubi [A] time = 0.0316454, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{x^3}{3}+x^2+4 x+9 \log (2-x) \]
Antiderivative was successfully verified.
[In] Int[(1 + x^3)/(-2 + x),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{x^{3}}{3} + 4 x + 9 \log{\left (- x + 2 \right )} + 2 \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**3+1)/(-2+x),x)
[Out]
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Mathematica [A] time = 0.0063875, size = 23, normalized size = 1.05 \[ \frac{x^3}{3}+x^2+4 x+9 \log (x-2)-\frac{44}{3} \]
Antiderivative was successfully verified.
[In] Integrate[(1 + x^3)/(-2 + x),x]
[Out]
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Maple [A] time = 0.003, size = 19, normalized size = 0.9 \[{\frac{{x}^{3}}{3}}+{x}^{2}+4\,x+9\,\ln \left ( x-2 \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^3+1)/(x-2),x)
[Out]
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Maxima [A] time = 0.813851, size = 24, normalized size = 1.09 \[ \frac{1}{3} \, x^{3} + x^{2} + 4 \, x + 9 \, \log \left (x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 + 1)/(x - 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.262207, size = 24, normalized size = 1.09 \[ \frac{1}{3} \, x^{3} + x^{2} + 4 \, x + 9 \, \log \left (x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 + 1)/(x - 2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.114196, size = 17, normalized size = 0.77 \[ \frac{x^{3}}{3} + x^{2} + 4 x + 9 \log{\left (x - 2 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**3+1)/(-2+x),x)
[Out]
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GIAC/XCAS [A] time = 0.259357, size = 26, normalized size = 1.18 \[ \frac{1}{3} \, x^{3} + x^{2} + 4 \, x + 9 \,{\rm ln}\left ({\left | x - 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 + 1)/(x - 2),x, algorithm="giac")
[Out]