Optimal. Leaf size=38 \[ -\frac {13}{5 (2 x+3)}-6 \log (x+1)+\frac {99}{25} \log (2 x+3)+\frac {51}{25} \log (3 x+2) \]
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Rubi [A] time = 0.03, antiderivative size = 38, 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 {13}{5 (2 x+3)}-6 \log (x+1)+\frac {99}{25} \log (2 x+3)+\frac {51}{25} \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)^2 \left (2+5 x+3 x^2\right )} \, dx &=\int \left (-\frac {6}{1+x}+\frac {26}{5 (3+2 x)^2}+\frac {198}{25 (3+2 x)}+\frac {153}{25 (2+3 x)}\right ) \, dx\\ &=-\frac {13}{5 (3+2 x)}-6 \log (1+x)+\frac {99}{25} \log (3+2 x)+\frac {51}{25} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.03, size = 38, normalized size = 1.00 \begin {gather*} \frac {1}{25} \left (-\frac {65}{2 x+3}+51 \log (-6 x-4)-150 \log (-2 (x+1))+99 \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)^2 \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 = 48, normalized size = 1.26 \begin {gather*} \frac {51 \, {\left (2 \, x + 3\right )} \log \left (3 \, x + 2\right ) + 99 \, {\left (2 \, x + 3\right )} \log \left (2 \, x + 3\right ) - 150 \, {\left (2 \, x + 3\right )} \log \left (x + 1\right ) - 65}{25 \, {\left (2 \, x + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 40, normalized size = 1.05 \begin {gather*} -\frac {13}{5 \, {\left (2 \, x + 3\right )}} - 6 \, \log \left ({\left | -\frac {1}{2 \, x + 3} + 1 \right |}\right ) + \frac {51}{25} \, \log \left ({\left | -\frac {5}{2 \, x + 3} + 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 33, normalized size = 0.87 \begin {gather*} \frac {51 \ln \left (3 x +2\right )}{25}+\frac {99 \ln \left (2 x +3\right )}{25}-6 \ln \left (x +1\right )-\frac {13}{5 \left (2 x +3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.73, size = 32, normalized size = 0.84 \begin {gather*} -\frac {13}{5 \, {\left (2 \, x + 3\right )}} + \frac {51}{25} \, \log \left (3 \, x + 2\right ) + \frac {99}{25} \, \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 = 2.29, size = 28, normalized size = 0.74 \begin {gather*} \frac {51\,\ln \left (x+\frac {2}{3}\right )}{25}-6\,\ln \left (x+1\right )+\frac {99\,\ln \left (x+\frac {3}{2}\right )}{25}-\frac {13}{10\,\left (x+\frac {3}{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 32, normalized size = 0.84 \begin {gather*} \frac {51 \log {\left (x + \frac {2}{3} \right )}}{25} - 6 \log {\left (x + 1 \right )} + \frac {99 \log {\left (x + \frac {3}{2} \right )}}{25} - \frac {13}{10 x + 15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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