Optimal. Leaf size=16 \[ 2 \log (1-x)-\frac{3}{x+1} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0495433, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042 \[ 2 \log (1-x)-\frac{3}{x+1} \]
Antiderivative was successfully verified.
[In] Int[(-1 + 7*x + 2*x^2)/(-1 - x + x^2 + x^3),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2*x**2+7*x-1)/(x**3+x**2-x-1),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0121834, size = 14, normalized size = 0.88 \[ 2 \log (x-1)-\frac{3}{x+1} \]
Antiderivative was successfully verified.
[In] Integrate[(-1 + 7*x + 2*x^2)/(-1 - x + x^2 + x^3),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.008, size = 15, normalized size = 0.9 \[ 2\,\ln \left ( -1+x \right ) -3\, \left ( 1+x \right ) ^{-1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2*x^2+7*x-1)/(x^3+x^2-x-1),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.786818, size = 19, normalized size = 1.19 \[ -\frac{3}{x + 1} + 2 \, \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x^2 + 7*x - 1)/(x^3 + x^2 - x - 1),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.251811, size = 23, normalized size = 1.44 \[ \frac{2 \,{\left (x + 1\right )} \log \left (x - 1\right ) - 3}{x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x^2 + 7*x - 1)/(x^3 + x^2 - x - 1),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.185855, size = 10, normalized size = 0.62 \[ 2 \log{\left (x - 1 \right )} - \frac{3}{x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x**2+7*x-1)/(x**3+x**2-x-1),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.262542, size = 20, normalized size = 1.25 \[ -\frac{3}{x + 1} + 2 \,{\rm ln}\left ({\left | x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x^2 + 7*x - 1)/(x^3 + x^2 - x - 1),x, algorithm="giac")
[Out]