Optimal. Leaf size=8 \[ -\log (1-x) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0117235, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ -\log (1-x) \]
Antiderivative was successfully verified.
[In] Int[(1 + x + x^2)/(1 - x^3),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 3.08812, size = 5, normalized size = 0.62 \[ - \log{\left (- x + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**2+x+1)/(-x**3+1),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00173559, size = 8, normalized size = 1. \[ -\log (1-x) \]
Antiderivative was successfully verified.
[In] Integrate[(1 + x + x^2)/(1 - x^3),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 7, normalized size = 0.9 \[ -\ln \left ( -1+x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^2+x+1)/(-x^3+1),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.36511, size = 8, normalized size = 1. \[ -\log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x^2 + x + 1)/(x^3 - 1),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.219915, size = 8, normalized size = 1. \[ -\log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x^2 + x + 1)/(x^3 - 1),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.045601, size = 5, normalized size = 0.62 \[ - \log{\left (x - 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**2+x+1)/(-x**3+1),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.217015, size = 9, normalized size = 1.12 \[ -{\rm ln}\left ({\left | x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x^2 + x + 1)/(x^3 - 1),x, algorithm="giac")
[Out]