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

Optimal. Leaf size=6 \[ \log (2-x) \]

[Out]

Log[2 - x]

_______________________________________________________________________________________

Rubi [A]  time = 0.0249443, antiderivative size = 6, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ \log (2-x) \]

Antiderivative was successfully verified.

[In]  Int[(x + x^2)/(-2*x - x^2 + x^3),x]

[Out]

Log[2 - x]

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 6.11693, size = 3, normalized size = 0.5 \[ \log{\left (- x + 2 \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((x**2+x)/(x**3-x**2-2*x),x)

[Out]

log(-x + 2)

_______________________________________________________________________________________

Mathematica [A]  time = 0.00123161, size = 4, normalized size = 0.67 \[ \log (x-2) \]

Antiderivative was successfully verified.

[In]  Integrate[(x + x^2)/(-2*x - x^2 + x^3),x]

[Out]

Log[-2 + x]

_______________________________________________________________________________________

Maple [A]  time = 0.001, size = 5, normalized size = 0.8 \[ \ln \left ( x-2 \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((x^2+x)/(x^3-x^2-2*x),x)

[Out]

ln(x-2)

_______________________________________________________________________________________

Maxima [A]  time = 0.781833, size = 5, normalized size = 0.83 \[ \log \left (x - 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 + x)/(x^3 - x^2 - 2*x),x, algorithm="maxima")

[Out]

log(x - 2)

_______________________________________________________________________________________

Fricas [A]  time = 0.252075, size = 5, normalized size = 0.83 \[ \log \left (x - 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 + x)/(x^3 - x^2 - 2*x),x, algorithm="fricas")

[Out]

log(x - 2)

_______________________________________________________________________________________

Sympy [A]  time = 0.084186, size = 3, normalized size = 0.5 \[ \log{\left (x - 2 \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x**2+x)/(x**3-x**2-2*x),x)

[Out]

log(x - 2)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.260901, size = 7, normalized size = 1.17 \[{\rm ln}\left ({\left | x - 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 + x)/(x^3 - x^2 - 2*x),x, algorithm="giac")

[Out]

ln(abs(x - 2))