Optimal. Leaf size=25 \[ \frac{3}{10} \log (2-x)-\frac{\log (x)}{6}-\frac{2}{15} \log (x+3) \]
[Out]
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Rubi [A] time = 0.0466046, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ \frac{3}{10} \log (2-x)-\frac{\log (x)}{6}-\frac{2}{15} \log (x+3) \]
Antiderivative was successfully verified.
[In] Int[(1 + x)/(-6*x + x^2 + x^3),x]
[Out]
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Rubi in Sympy [A] time = 9.82311, size = 20, normalized size = 0.8 \[ - \frac{\log{\left (x \right )}}{6} + \frac{3 \log{\left (- x + 2 \right )}}{10} - \frac{2 \log{\left (x + 3 \right )}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x)/(x**3+x**2-6*x),x)
[Out]
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Mathematica [A] time = 0.00781111, size = 25, normalized size = 1. \[ \frac{3}{10} \log (2-x)-\frac{\log (x)}{6}-\frac{2}{15} \log (x+3) \]
Antiderivative was successfully verified.
[In] Integrate[(1 + x)/(-6*x + x^2 + x^3),x]
[Out]
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Maple [A] time = 0.01, size = 18, normalized size = 0.7 \[ -{\frac{\ln \left ( x \right ) }{6}}+{\frac{3\,\ln \left ( x-2 \right ) }{10}}-{\frac{2\,\ln \left ( 3+x \right ) }{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x)/(x^3+x^2-6*x),x)
[Out]
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Maxima [A] time = 0.793163, size = 23, normalized size = 0.92 \[ -\frac{2}{15} \, \log \left (x + 3\right ) + \frac{3}{10} \, \log \left (x - 2\right ) - \frac{1}{6} \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)/(x^3 + x^2 - 6*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.25752, size = 23, normalized size = 0.92 \[ -\frac{2}{15} \, \log \left (x + 3\right ) + \frac{3}{10} \, \log \left (x - 2\right ) - \frac{1}{6} \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)/(x^3 + x^2 - 6*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.298799, size = 20, normalized size = 0.8 \[ - \frac{\log{\left (x \right )}}{6} + \frac{3 \log{\left (x - 2 \right )}}{10} - \frac{2 \log{\left (x + 3 \right )}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1+x)/(x**3+x**2-6*x),x)
[Out]
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GIAC/XCAS [A] time = 0.263813, size = 27, normalized size = 1.08 \[ -\frac{2}{15} \,{\rm ln}\left ({\left | x + 3 \right |}\right ) + \frac{3}{10} \,{\rm ln}\left ({\left | x - 2 \right |}\right ) - \frac{1}{6} \,{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)/(x^3 + x^2 - 6*x),x, algorithm="giac")
[Out]