Optimal. Leaf size=15 \[ \log (x)-\frac{1}{2} \log \left (1-x^2\right ) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0208824, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 5, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.556 \[ \log (x)-\frac{1}{2} \log \left (1-x^2\right ) \]
Antiderivative was successfully verified.
[In] Int[(x - x^3)^(-1),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-x**3+x),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00394251, size = 15, normalized size = 1. \[ \log (x)-\frac{1}{2} \log \left (1-x^2\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(x - x^3)^(-1),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.009, size = 16, normalized size = 1.1 \[ \ln \left ( x \right ) -{\frac{\ln \left ( -1+x \right ) }{2}}-{\frac{\ln \left ( 1+x \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(-x^3+x),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.36284, size = 20, normalized size = 1.33 \[ -\frac{1}{2} \, \log \left (x + 1\right ) - \frac{1}{2} \, \log \left (x - 1\right ) + \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/(x^3 - x),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.201793, size = 15, normalized size = 1. \[ -\frac{1}{2} \, \log \left (x^{2} - 1\right ) + \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/(x^3 - x),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.175263, size = 10, normalized size = 0.67 \[ \log{\left (x \right )} - \frac{\log{\left (x^{2} - 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-x**3+x),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.221381, size = 22, normalized size = 1.47 \[ \frac{1}{2} \,{\rm ln}\left (x^{2}\right ) - \frac{1}{2} \,{\rm ln}\left ({\left | x^{2} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/(x^3 - x),x, algorithm="giac")
[Out]