Optimal. Leaf size=17 \[ 2 \log (1-x)+\log (x)+3 \log (x+3) \]
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Rubi [A] time = 0.04, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {1594, 1628} \[ 2 \log (1-x)+\log (x)+3 \log (x+3) \]
Antiderivative was successfully verified.
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Rule 1594
Rule 1628
Rubi steps
\begin {align*} \int \frac {-3+5 x+6 x^2}{-3 x+2 x^2+x^3} \, dx &=\int \frac {-3+5 x+6 x^2}{x \left (-3+2 x+x^2\right )} \, dx\\ &=\int \left (\frac {2}{-1+x}+\frac {1}{x}+\frac {3}{3+x}\right ) \, dx\\ &=2 \log (1-x)+\log (x)+3 \log (3+x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 1.00 \[ 2 \log (1-x)+\log (x)+3 \log (x+3) \]
Antiderivative was successfully verified.
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fricas [A] time = 1.13, size = 15, normalized size = 0.88 \[ 3 \, \log \left (x + 3\right ) + 2 \, \log \left (x - 1\right ) + \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.38, size = 18, normalized size = 1.06 \[ 3 \, \log \left ({\left | x + 3 \right |}\right ) + 2 \, \log \left ({\left | x - 1 \right |}\right ) + \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 16, normalized size = 0.94 \[ \ln \relax (x )+2 \ln \left (x -1\right )+3 \ln \left (x +3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.85, size = 15, normalized size = 0.88 \[ 3 \, \log \left (x + 3\right ) + 2 \, \log \left (x - 1\right ) + \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 15, normalized size = 0.88 \[ 2\,\ln \left (x-1\right )+3\,\ln \left (x+3\right )+\ln \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 15, normalized size = 0.88 \[ \log {\relax (x )} + 2 \log {\left (x - 1 \right )} + 3 \log {\left (x + 3 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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