Optimal. Leaf size=29 \[ \frac{x^2}{2}+6 x+\frac{85}{2} \log (7-x)+\frac{1}{2} \log (x+1) \]
[Out]
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Rubi [A] time = 0.0359319, antiderivative size = 29, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 3, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.188 \[ \frac{x^2}{2}+6 x+\frac{85}{2} \log (7-x)+\frac{1}{2} \log (x+1) \]
Antiderivative was successfully verified.
[In] Int[(-3 + x^3)/(-7 - 6*x + x^2),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ 6 x + \frac{85 \log{\left (- x + 7 \right )}}{2} + \frac{\log{\left (x + 1 \right )}}{2} + \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**3-3)/(x**2-6*x-7),x)
[Out]
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Mathematica [A] time = 0.00906544, size = 29, normalized size = 1. \[ \frac{x^2}{2}+6 x+\frac{85}{2} \log (7-x)+\frac{1}{2} \log (x+1) \]
Antiderivative was successfully verified.
[In] Integrate[(-3 + x^3)/(-7 - 6*x + x^2),x]
[Out]
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Maple [A] time = 0.008, size = 22, normalized size = 0.8 \[{\frac{{x}^{2}}{2}}+6\,x+{\frac{\ln \left ( 1+x \right ) }{2}}+{\frac{85\,\ln \left ( x-7 \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^3-3)/(x^2-6*x-7),x)
[Out]
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Maxima [A] time = 0.825232, size = 28, normalized size = 0.97 \[ \frac{1}{2} \, x^{2} + 6 \, x + \frac{1}{2} \, \log \left (x + 1\right ) + \frac{85}{2} \, \log \left (x - 7\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 - 3)/(x^2 - 6*x - 7),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.253094, size = 28, normalized size = 0.97 \[ \frac{1}{2} \, x^{2} + 6 \, x + \frac{1}{2} \, \log \left (x + 1\right ) + \frac{85}{2} \, \log \left (x - 7\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 - 3)/(x^2 - 6*x - 7),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.212784, size = 22, normalized size = 0.76 \[ \frac{x^{2}}{2} + 6 x + \frac{85 \log{\left (x - 7 \right )}}{2} + \frac{\log{\left (x + 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**3-3)/(x**2-6*x-7),x)
[Out]
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GIAC/XCAS [A] time = 0.261119, size = 31, normalized size = 1.07 \[ \frac{1}{2} \, x^{2} + 6 \, x + \frac{1}{2} \,{\rm ln}\left ({\left | x + 1 \right |}\right ) + \frac{85}{2} \,{\rm ln}\left ({\left | x - 7 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 - 3)/(x^2 - 6*x - 7),x, algorithm="giac")
[Out]