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 = 0.04, antiderivative size = 41, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, 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*}
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Mathematica [A] time = 0.02, size = 37, normalized size = 0.90 \[ -\frac {407}{16 (x-3)}-\frac {133}{8 (x-3)^2}+\frac {313}{64} \log (3-x)+\frac {7}{64} \log (x+1) \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.03, size = 31, normalized size = 0.76 \[ \frac {955-407 x}{16 (x-3)^2}+\frac {313}{64} \log (x-3)+\frac {7}{64} \log (x+1) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.89, size = 45, normalized size = 1.10 \[ \frac {7 \, {\left (x^{2} - 6 \, x + 9\right )} \log \left (x + 1\right ) + 313 \, {\left (x^{2} - 6 \, x + 9\right )} \log \left (x - 3\right ) - 1628 \, x + 3820}{64 \, {\left (x^{2} - 6 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.88, size = 27, normalized size = 0.66 \[ -\frac {407 \, x - 955}{16 \, {\left (x - 3\right )}^{2}} + \frac {7}{64} \, \log \left ({\left | x + 1 \right |}\right ) + \frac {313}{64} \, \log \left ({\left | x - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 25, normalized size = 0.61
method | result | size |
norman | \(\frac {-\frac {407 x}{16}+\frac {955}{16}}{\left (-3+x \right )^{2}}+\frac {313 \ln \left (-3+x \right )}{64}+\frac {7 \ln \left (1+x \right )}{64}\) | \(25\) |
default | \(-\frac {133}{8 \left (-3+x \right )^{2}}-\frac {407}{16 \left (-3+x \right )}+\frac {313 \ln \left (-3+x \right )}{64}+\frac {7 \ln \left (1+x \right )}{64}\) | \(28\) |
risch | \(\frac {-\frac {407 x}{16}+\frac {955}{16}}{x^{2}-6 x +9}+\frac {313 \ln \left (-3+x \right )}{64}+\frac {7 \ln \left (1+x \right )}{64}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 30, normalized size = 0.73 \[ -\frac {407 \, x - 955}{16 \, {\left (x^{2} - 6 \, x + 9\right )}} + \frac {7}{64} \, \log \left (x + 1\right ) + \frac {313}{64} \, \log \left (x - 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 30, normalized size = 0.73 \[ \frac {7\,\ln \left (x+1\right )}{64}+\frac {313\,\ln \left (x-3\right )}{64}-\frac {\frac {407\,x}{16}-\frac {955}{16}}{x^2-6\,x+9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 31, normalized size = 0.76 \[ \frac {955 - 407 x}{16 x^{2} - 96 x + 144} + \frac {313 \log {\left (x - 3 \right )}}{64} + \frac {7 \log {\left (x + 1 \right )}}{64} \]
Verification of antiderivative is not currently implemented for this CAS.
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