Optimal. Leaf size=19 \[ \frac{1}{4} \log \left (2-x^2\right )+\frac{\log (x)}{2} \]
[Out]
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Rubi [A] time = 0.0496399, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ \frac{1}{4} \log \left (2-x^2\right )+\frac{\log (x)}{2} \]
Antiderivative was successfully verified.
[In] Int[(-1 + x^2)/(-2*x + x^3),x]
[Out]
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Rubi in Sympy [A] time = 8.20481, size = 14, normalized size = 0.74 \[ \frac{\log{\left (x^{2} \right )}}{4} + \frac{\log{\left (- x^{2} + 2 \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**2-1)/(x**3-2*x),x)
[Out]
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Mathematica [A] time = 0.00559458, size = 19, normalized size = 1. \[ \frac{1}{4} \log \left (2-x^2\right )+\frac{\log (x)}{2} \]
Antiderivative was successfully verified.
[In] Integrate[(-1 + x^2)/(-2*x + x^3),x]
[Out]
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Maple [A] time = 0.007, size = 14, normalized size = 0.7 \[{\frac{\ln \left ( x \right ) }{2}}+{\frac{\ln \left ({x}^{2}-2 \right ) }{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^2-1)/(x^3-2*x),x)
[Out]
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Maxima [A] time = 0.78842, size = 18, normalized size = 0.95 \[ \frac{1}{4} \, \log \left (x^{2} - 2\right ) + \frac{1}{2} \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - 1)/(x^3 - 2*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.258814, size = 18, normalized size = 0.95 \[ \frac{1}{4} \, \log \left (x^{2} - 2\right ) + \frac{1}{2} \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - 1)/(x^3 - 2*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.178408, size = 12, normalized size = 0.63 \[ \frac{\log{\left (x \right )}}{2} + \frac{\log{\left (x^{2} - 2 \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**2-1)/(x**3-2*x),x)
[Out]
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GIAC/XCAS [A] time = 0.259422, size = 22, normalized size = 1.16 \[ \frac{1}{4} \,{\rm ln}\left (x^{2}\right ) + \frac{1}{4} \,{\rm ln}\left ({\left | x^{2} - 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - 1)/(x^3 - 2*x),x, algorithm="giac")
[Out]