Optimal. Leaf size=20 \[ x+\frac{4}{5} \log (2-x)-\frac{9}{5} \log (x+3) \]
[Out]
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Rubi [A] time = 0.0292592, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25 \[ x+\frac{4}{5} \log (2-x)-\frac{9}{5} \log (x+3) \]
Antiderivative was successfully verified.
[In] Int[x^2/(-6 + x + x^2),x]
[Out]
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Rubi in Sympy [A] time = 6.4841, size = 17, normalized size = 0.85 \[ x + \frac{4 \log{\left (- x + 2 \right )}}{5} - \frac{9 \log{\left (x + 3 \right )}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/(x**2+x-6),x)
[Out]
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Mathematica [A] time = 0.0063971, size = 20, normalized size = 1. \[ x+\frac{4}{5} \log (2-x)-\frac{9}{5} \log (x+3) \]
Antiderivative was successfully verified.
[In] Integrate[x^2/(-6 + x + x^2),x]
[Out]
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Maple [A] time = 0.008, size = 15, normalized size = 0.8 \[ x-{\frac{9\,\ln \left ( 3+x \right ) }{5}}+{\frac{4\,\ln \left ( x-2 \right ) }{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/(x^2+x-6),x)
[Out]
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Maxima [A] time = 0.670454, size = 19, normalized size = 0.95 \[ x - \frac{9}{5} \, \log \left (x + 3\right ) + \frac{4}{5} \, \log \left (x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(x^2 + x - 6),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.207884, size = 19, normalized size = 0.95 \[ x - \frac{9}{5} \, \log \left (x + 3\right ) + \frac{4}{5} \, \log \left (x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(x^2 + x - 6),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.1977, size = 17, normalized size = 0.85 \[ x + \frac{4 \log{\left (x - 2 \right )}}{5} - \frac{9 \log{\left (x + 3 \right )}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2/(x**2+x-6),x)
[Out]
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GIAC/XCAS [A] time = 0.203356, size = 22, normalized size = 1.1 \[ x - \frac{9}{5} \,{\rm ln}\left ({\left | x + 3 \right |}\right ) + \frac{4}{5} \,{\rm ln}\left ({\left | x - 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(x^2 + x - 6),x, algorithm="giac")
[Out]