3.50 \(\int \frac{1+x+x^2}{1-x^3} \, dx\)

Optimal. Leaf size=8 \[ -\log (1-x) \]

[Out]

-Log[1 - x]

_______________________________________________________________________________________

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]

-Log[1 - x]

_______________________________________________________________________________________

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]

-log(-x + 1)

_______________________________________________________________________________________

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]

-Log[1 - x]

_______________________________________________________________________________________

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]

-ln(-1+x)

_______________________________________________________________________________________

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]

-log(x - 1)

_______________________________________________________________________________________

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]

-log(x - 1)

_______________________________________________________________________________________

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]

-log(x - 1)

_______________________________________________________________________________________

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]

-ln(abs(x - 1))