Optimal. Leaf size=2 \[ \tanh ^{-1}(x) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.00725849, antiderivative size = 2, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \tanh ^{-1}(x) \]
Antiderivative was successfully verified.
[In] Int[x/(x - x^3),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 1.07745, size = 2, normalized size = 1. \[ \operatorname{atanh}{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(-x**3+x),x)
[Out]
_______________________________________________________________________________________
Mathematica [B] time = 0.00355821, size = 19, normalized size = 9.5 \[ \frac{1}{2} \log (x+1)-\frac{1}{2} \log (1-x) \]
Antiderivative was successfully verified.
[In] Integrate[x/(x - x^3),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.001, size = 3, normalized size = 1.5 \[{\it Artanh} \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(-x^3+x),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.36441, size = 18, normalized size = 9. \[ \frac{1}{2} \, \log \left (x + 1\right ) - \frac{1}{2} \, \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-x/(x^3 - x),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.203402, size = 18, normalized size = 9. \[ \frac{1}{2} \, \log \left (x + 1\right ) - \frac{1}{2} \, \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-x/(x^3 - x),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.176834, size = 12, normalized size = 6. \[ - \frac{\log{\left (x - 1 \right )}}{2} + \frac{\log{\left (x + 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(-x**3+x),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.218752, size = 20, normalized size = 10. \[ \frac{1}{2} \,{\rm ln}\left ({\left | x + 1 \right |}\right ) - \frac{1}{2} \,{\rm ln}\left ({\left | x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-x/(x^3 - x),x, algorithm="giac")
[Out]