Optimal. Leaf size=41 \[ \frac{407}{16 (3-x)}-\frac{133}{8 (3-x)^2}+\frac{313}{64} \log (3-x)+\frac{7}{64} \log (x+1) \]
[Out]
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Rubi [A] time = 0.06588, antiderivative size = 41, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.04 \[ \frac{407}{16 (3-x)}-\frac{133}{8 (3-x)^2}+\frac{313}{64} \log (3-x)+\frac{7}{64} \log (x+1) \]
Antiderivative was successfully verified.
[In] Int[(-2 + 5*x^3)/(-27 + 18*x^2 - 8*x^3 + x^4),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{5 x^{3} - 2}{x^{4} - 8 x^{3} + 18 x^{2} - 27}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((5*x**3-2)/(x**4-8*x**3+18*x**2-27),x)
[Out]
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Mathematica [A] time = 0.0318054, size = 37, normalized size = 0.9 \[ -\frac{407}{16 (x-3)}-\frac{133}{8 (x-3)^2}+\frac{313}{64} \log (3-x)+\frac{7}{64} \log (x+1) \]
Antiderivative was successfully verified.
[In] Integrate[(-2 + 5*x^3)/(-27 + 18*x^2 - 8*x^3 + x^4),x]
[Out]
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Maple [A] time = 0.011, size = 28, normalized size = 0.7 \[ -{\frac{133}{8\, \left ( -3+x \right ) ^{2}}}-{\frac{407}{-48+16\,x}}+{\frac{313\,\ln \left ( -3+x \right ) }{64}}+{\frac{7\,\ln \left ( 1+x \right ) }{64}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((5*x^3-2)/(x^4-8*x^3+18*x^2-27),x)
[Out]
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Maxima [A] time = 1.33897, size = 41, normalized size = 1. \[ -\frac{407 \, x - 955}{16 \,{\left (x^{2} - 6 \, x + 9\right )}} + \frac{7}{64} \, \log \left (x + 1\right ) + \frac{313}{64} \, \log \left (x - 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x^3 - 2)/(x^4 - 8*x^3 + 18*x^2 - 27),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.198308, size = 61, normalized size = 1.49 \[ \frac{7 \,{\left (x^{2} - 6 \, x + 9\right )} \log \left (x + 1\right ) + 313 \,{\left (x^{2} - 6 \, x + 9\right )} \log \left (x - 3\right ) - 1628 \, x + 3820}{64 \,{\left (x^{2} - 6 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x^3 - 2)/(x^4 - 8*x^3 + 18*x^2 - 27),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.150699, size = 31, normalized size = 0.76 \[ - \frac{407 x - 955}{16 x^{2} - 96 x + 144} + \frac{313 \log{\left (x - 3 \right )}}{64} + \frac{7 \log{\left (x + 1 \right )}}{64} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x**3-2)/(x**4-8*x**3+18*x**2-27),x)
[Out]
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GIAC/XCAS [A] time = 0.1998, size = 36, normalized size = 0.88 \[ -\frac{407 \, x - 955}{16 \,{\left (x - 3\right )}^{2}} + \frac{7}{64} \,{\rm ln}\left ({\left | x + 1 \right |}\right ) + \frac{313}{64} \,{\rm ln}\left ({\left | x - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x^3 - 2)/(x^4 - 8*x^3 + 18*x^2 - 27),x, algorithm="giac")
[Out]