Optimal. Leaf size=27 \[ -6 \log (x+1)+\frac {13}{5} \log (2 x+3)+\frac {17}{5} \log (3 x+2) \]
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Rubi [A] time = 0.03, antiderivative size = 27, 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 = {800} \begin {gather*} -6 \log (x+1)+\frac {13}{5} \log (2 x+3)+\frac {17}{5} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
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Rule 800
Rubi steps
\begin {align*} \int \frac {5-x}{(3+2 x) \left (2+5 x+3 x^2\right )} \, dx &=\int \left (-\frac {6}{1+x}+\frac {26}{5 (3+2 x)}+\frac {51}{5 (2+3 x)}\right ) \, dx\\ &=-6 \log (1+x)+\frac {13}{5} \log (3+2 x)+\frac {17}{5} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 27, normalized size = 1.00 \begin {gather*} -6 \log (x+1)+\frac {13}{5} \log (2 x+3)+\frac {17}{5} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {5-x}{(3+2 x) \left (2+5 x+3 x^2\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.38, size = 23, normalized size = 0.85 \begin {gather*} \frac {17}{5} \, \log \left (3 \, x + 2\right ) + \frac {13}{5} \, \log \left (2 \, x + 3\right ) - 6 \, \log \left (x + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 26, normalized size = 0.96 \begin {gather*} \frac {17}{5} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) + \frac {13}{5} \, \log \left ({\left | 2 \, x + 3 \right |}\right ) - 6 \, \log \left ({\left | x + 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 24, normalized size = 0.89 \begin {gather*} \frac {17 \ln \left (3 x +2\right )}{5}+\frac {13 \ln \left (2 x +3\right )}{5}-6 \ln \left (x +1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 23, normalized size = 0.85 \begin {gather*} \frac {17}{5} \, \log \left (3 \, x + 2\right ) + \frac {13}{5} \, \log \left (2 \, x + 3\right ) - 6 \, \log \left (x + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 19, normalized size = 0.70 \begin {gather*} \frac {17\,\ln \left (x+\frac {2}{3}\right )}{5}-6\,\ln \left (x+1\right )+\frac {13\,\ln \left (x+\frac {3}{2}\right )}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 26, normalized size = 0.96 \begin {gather*} \frac {17 \log {\left (x + \frac {2}{3} \right )}}{5} - 6 \log {\left (x + 1 \right )} + \frac {13 \log {\left (x + \frac {3}{2} \right )}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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