Optimal. Leaf size=66 \[ -\frac {3 (47 x+37)}{5 (2 x+3) \left (3 x^2+5 x+2\right )}-\frac {454}{25 (2 x+3)}+11 \log (x+1)+\frac {812}{125} \log (2 x+3)-\frac {2187}{125} \log (3 x+2) \]
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Rubi [A] time = 0.05, antiderivative size = 66, 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 = {822, 800} \[ -\frac {3 (47 x+37)}{5 (2 x+3) \left (3 x^2+5 x+2\right )}-\frac {454}{25 (2 x+3)}+11 \log (x+1)+\frac {812}{125} \log (2 x+3)-\frac {2187}{125} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 800
Rule 822
Rubi steps
\begin {align*} \int \frac {5-x}{(3+2 x)^2 \left (2+5 x+3 x^2\right )^2} \, dx &=-\frac {3 (37+47 x)}{5 (3+2 x) \left (2+5 x+3 x^2\right )}-\frac {1}{5} \int \frac {619+564 x}{(3+2 x)^2 \left (2+5 x+3 x^2\right )} \, dx\\ &=-\frac {3 (37+47 x)}{5 (3+2 x) \left (2+5 x+3 x^2\right )}-\frac {1}{5} \int \left (-\frac {55}{1+x}-\frac {908}{5 (3+2 x)^2}-\frac {1624}{25 (3+2 x)}+\frac {6561}{25 (2+3 x)}\right ) \, dx\\ &=-\frac {454}{25 (3+2 x)}-\frac {3 (37+47 x)}{5 (3+2 x) \left (2+5 x+3 x^2\right )}+11 \log (1+x)+\frac {812}{125} \log (3+2 x)-\frac {2187}{125} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.03, size = 57, normalized size = 0.86 \[ \frac {1}{125} \left (-\frac {15 (201 x+151)}{3 x^2+5 x+2}-\frac {260}{2 x+3}-2187 \log (-6 x-4)+1375 \log (-2 (x+1))+812 \log (2 x+3)\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.70, size = 96, normalized size = 1.45 \[ -\frac {6810 \, x^{2} + 2187 \, {\left (6 \, x^{3} + 19 \, x^{2} + 19 \, x + 6\right )} \log \left (3 \, x + 2\right ) - 812 \, {\left (6 \, x^{3} + 19 \, x^{2} + 19 \, x + 6\right )} \log \left (2 \, x + 3\right ) - 1375 \, {\left (6 \, x^{3} + 19 \, x^{2} + 19 \, x + 6\right )} \log \left (x + 1\right ) + 14875 \, x + 7315}{125 \, {\left (6 \, x^{3} + 19 \, x^{2} + 19 \, x + 6\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 77, normalized size = 1.17 \[ -\frac {52}{25 \, {\left (2 \, x + 3\right )}} + \frac {6 \, {\left (\frac {1403}{2 \, x + 3} - 903\right )}}{125 \, {\left (\frac {5}{2 \, x + 3} - 3\right )} {\left (\frac {1}{2 \, x + 3} - 1\right )}} + 11 \, \log \left ({\left | -\frac {1}{2 \, x + 3} + 1 \right |}\right ) - \frac {2187}{125} \, \log \left ({\left | -\frac {5}{2 \, x + 3} + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 49, normalized size = 0.74 \[ -\frac {2187 \ln \left (3 x +2\right )}{125}+\frac {812 \ln \left (2 x +3\right )}{125}+11 \ln \left (x +1\right )-\frac {153}{25 \left (3 x +2\right )}-\frac {52}{25 \left (2 x +3\right )}-\frac {6}{x +1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 52, normalized size = 0.79 \[ -\frac {1362 \, x^{2} + 2975 \, x + 1463}{25 \, {\left (6 \, x^{3} + 19 \, x^{2} + 19 \, x + 6\right )}} - \frac {2187}{125} \, \log \left (3 \, x + 2\right ) + \frac {812}{125} \, \log \left (2 \, x + 3\right ) + 11 \, \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.32, size = 46, normalized size = 0.70 \[ 11\,\ln \left (x+1\right )-\frac {2187\,\ln \left (x+\frac {2}{3}\right )}{125}+\frac {812\,\ln \left (x+\frac {3}{2}\right )}{125}-\frac {\frac {227\,x^2}{25}+\frac {119\,x}{6}+\frac {1463}{150}}{x^3+\frac {19\,x^2}{6}+\frac {19\,x}{6}+1} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 51, normalized size = 0.77 \[ - \frac {1362 x^{2} + 2975 x + 1463}{150 x^{3} + 475 x^{2} + 475 x + 150} - \frac {2187 \log {\left (x + \frac {2}{3} \right )}}{125} + 11 \log {\left (x + 1 \right )} + \frac {812 \log {\left (x + \frac {3}{2} \right )}}{125} \]
Verification of antiderivative is not currently implemented for this CAS.
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