Optimal. Leaf size=18 \[ x-12 \log (2-x)+17 \log (3-x) \]
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Rubi [A] time = 0.02, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 3, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.188, Rules used = {1657, 632, 31} \[ x-12 \log (2-x)+17 \log (3-x) \]
Antiderivative was successfully verified.
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Rule 31
Rule 632
Rule 1657
Rubi steps
\begin {align*} \int \frac {8+x^2}{6-5 x+x^2} \, dx &=\int \left (1+\frac {2+5 x}{6-5 x+x^2}\right ) \, dx\\ &=x+\int \frac {2+5 x}{6-5 x+x^2} \, dx\\ &=x-12 \int \frac {1}{-2+x} \, dx+17 \int \frac {1}{-3+x} \, dx\\ &=x-12 \log (2-x)+17 \log (3-x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 18, normalized size = 1.00 \[ x-12 \log (2-x)+17 \log (3-x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 14, normalized size = 0.78 \[ x - 12 \, \log \left (x - 2\right ) + 17 \, \log \left (x - 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 16, normalized size = 0.89 \[ x - 12 \, \log \left ({\left | x - 2 \right |}\right ) + 17 \, \log \left ({\left | x - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 15, normalized size = 0.83 \[ x +17 \ln \left (x -3\right )-12 \ln \left (x -2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 14, normalized size = 0.78 \[ x - 12 \, \log \left (x - 2\right ) + 17 \, \log \left (x - 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.92, size = 14, normalized size = 0.78 \[ x-12\,\ln \left (x-2\right )+17\,\ln \left (x-3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 14, normalized size = 0.78 \[ x + 17 \log {\left (x - 3 \right )} - 12 \log {\left (x - 2 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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