Optimal. Leaf size=49 \[ -\frac {99}{25 (2 x+3)}-\frac {13}{10 (2 x+3)^2}-6 \log (x+1)+\frac {597}{125} \log (2 x+3)+\frac {153}{125} \log (3 x+2) \]
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Rubi [A] time = 0.03, antiderivative size = 49, 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*} -\frac {99}{25 (2 x+3)}-\frac {13}{10 (2 x+3)^2}-6 \log (x+1)+\frac {597}{125} \log (2 x+3)+\frac {153}{125} \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)^3 \left (2+5 x+3 x^2\right )} \, dx &=\int \left (-\frac {6}{1+x}+\frac {26}{5 (3+2 x)^3}+\frac {198}{25 (3+2 x)^2}+\frac {1194}{125 (3+2 x)}+\frac {459}{125 (2+3 x)}\right ) \, dx\\ &=-\frac {13}{10 (3+2 x)^2}-\frac {99}{25 (3+2 x)}-6 \log (1+x)+\frac {597}{125} \log (3+2 x)+\frac {153}{125} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.03, size = 47, normalized size = 0.96 \begin {gather*} \frac {1}{250} \left (-\frac {990}{2 x+3}-\frac {325}{(2 x+3)^2}+306 \log (-6 x-4)-1500 \log (-2 (x+1))+1194 \log (2 x+3)\right ) \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)^3 \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 = 0.39, size = 71, normalized size = 1.45 \begin {gather*} \frac {306 \, {\left (4 \, x^{2} + 12 \, x + 9\right )} \log \left (3 \, x + 2\right ) + 1194 \, {\left (4 \, x^{2} + 12 \, x + 9\right )} \log \left (2 \, x + 3\right ) - 1500 \, {\left (4 \, x^{2} + 12 \, x + 9\right )} \log \left (x + 1\right ) - 1980 \, x - 3295}{250 \, {\left (4 \, x^{2} + 12 \, x + 9\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 40, normalized size = 0.82 \begin {gather*} -\frac {396 \, x + 659}{50 \, {\left (2 \, x + 3\right )}^{2}} + \frac {153}{125} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) + \frac {597}{125} \, \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 = 42, normalized size = 0.86 \begin {gather*} \frac {153 \ln \left (3 x +2\right )}{125}+\frac {597 \ln \left (2 x +3\right )}{125}-6 \ln \left (x +1\right )-\frac {13}{10 \left (2 x +3\right )^{2}}-\frac {99}{25 \left (2 x +3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.58, size = 42, normalized size = 0.86 \begin {gather*} -\frac {396 \, x + 659}{50 \, {\left (4 \, x^{2} + 12 \, x + 9\right )}} + \frac {153}{125} \, \log \left (3 \, x + 2\right ) + \frac {597}{125} \, \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 = 0.04, size = 36, normalized size = 0.73 \begin {gather*} \frac {153\,\ln \left (x+\frac {2}{3}\right )}{125}-6\,\ln \left (x+1\right )+\frac {597\,\ln \left (x+\frac {3}{2}\right )}{125}-\frac {\frac {99\,x}{50}+\frac {659}{200}}{x^2+3\,x+\frac {9}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 41, normalized size = 0.84 \begin {gather*} - \frac {396 x + 659}{200 x^{2} + 600 x + 450} + \frac {153 \log {\left (x + \frac {2}{3} \right )}}{125} - 6 \log {\left (x + 1 \right )} + \frac {597 \log {\left (x + \frac {3}{2} \right )}}{125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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