Optimal. Leaf size=41 \[ \frac{407}{16 (3-x)}-\frac{133}{8 (3-x)^2}+\frac{313}{64} \log (3-x)+\frac{7}{64} \log (x+1) \]
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Rubi [A] time = 0.0370383, 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, Rules used = {2074} \[ \frac{407}{16 (3-x)}-\frac{133}{8 (3-x)^2}+\frac{313}{64} \log (3-x)+\frac{7}{64} \log (x+1) \]
Antiderivative was successfully verified.
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Rule 2074
Rubi steps
\begin{align*} \int \frac{-2+5 x^3}{-27+18 x^2-8 x^3+x^4} \, dx &=\int \left (\frac{133}{4 (-3+x)^3}+\frac{407}{16 (-3+x)^2}+\frac{313}{64 (-3+x)}+\frac{7}{64 (1+x)}\right ) \, dx\\ &=-\frac{133}{8 (3-x)^2}+\frac{407}{16 (3-x)}+\frac{313}{64} \log (3-x)+\frac{7}{64} \log (1+x)\\ \end{align*}
Mathematica [A] time = 0.019543, 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.
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Maple [A] time = 0.007, size = 28, normalized size = 0.7 \begin{align*}{\frac{7\,\ln \left ( 1+x \right ) }{64}}-{\frac{133}{8\, \left ( -3+x \right ) ^{2}}}-{\frac{407}{-48+16\,x}}+{\frac{313\,\ln \left ( -3+x \right ) }{64}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.933254, size = 41, normalized size = 1. \begin{align*} -\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 ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.08478, size = 138, normalized size = 3.37 \begin{align*} \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 )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.123652, size = 31, normalized size = 0.76 \begin{align*} - \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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05388, size = 36, normalized size = 0.88 \begin{align*} -\frac{407 \, x - 955}{16 \,{\left (x - 3\right )}^{2}} + \frac{7}{64} \, \log \left ({\left | x + 1 \right |}\right ) + \frac{313}{64} \, \log \left ({\left | x - 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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