Optimal. Leaf size=94 \[ -\frac {3 (47 x+37)}{10 (2 x+3) \left (3 x^2+5 x+2\right )^2}+\frac {10848 x+9293}{50 (2 x+3) \left (3 x^2+5 x+2\right )}+\frac {12946}{125 (2 x+3)}-175 \log (x+1)+\frac {4912}{625} \log (2 x+3)+\frac {104463}{625} \log (3 x+2) \]
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Rubi [A] time = 0.06, antiderivative size = 94, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 2, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {822, 800} \begin {gather*} -\frac {3 (47 x+37)}{10 (2 x+3) \left (3 x^2+5 x+2\right )^2}+\frac {10848 x+9293}{50 (2 x+3) \left (3 x^2+5 x+2\right )}+\frac {12946}{125 (2 x+3)}-175 \log (x+1)+\frac {4912}{625} \log (2 x+3)+\frac {104463}{625} \log (3 x+2) \end {gather*}
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 )^3} \, dx &=-\frac {3 (37+47 x)}{10 (3+2 x) \left (2+5 x+3 x^2\right )^2}-\frac {1}{10} \int \frac {1439+1128 x}{(3+2 x)^2 \left (2+5 x+3 x^2\right )^2} \, dx\\ &=-\frac {3 (37+47 x)}{10 (3+2 x) \left (2+5 x+3 x^2\right )^2}+\frac {9293+10848 x}{50 (3+2 x) \left (2+5 x+3 x^2\right )}+\frac {1}{50} \int \frac {52142+43392 x}{(3+2 x)^2 \left (2+5 x+3 x^2\right )} \, dx\\ &=-\frac {3 (37+47 x)}{10 (3+2 x) \left (2+5 x+3 x^2\right )^2}+\frac {9293+10848 x}{50 (3+2 x) \left (2+5 x+3 x^2\right )}+\frac {1}{50} \int \left (-\frac {8750}{1+x}-\frac {51784}{5 (3+2 x)^2}+\frac {19648}{25 (3+2 x)}+\frac {626778}{25 (2+3 x)}\right ) \, dx\\ &=\frac {12946}{125 (3+2 x)}-\frac {3 (37+47 x)}{10 (3+2 x) \left (2+5 x+3 x^2\right )^2}+\frac {9293+10848 x}{50 (3+2 x) \left (2+5 x+3 x^2\right )}-175 \log (1+x)+\frac {4912}{625} \log (3+2 x)+\frac {104463}{625} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.04, size = 78, normalized size = 0.83 \begin {gather*} \frac {1}{625} \left (-\frac {75 (201 x+151)}{2 \left (3 x^2+5 x+2\right )^2}+\frac {5 (39462 x+33697)}{6 x^2+10 x+4}-\frac {1040}{2 x+3}+104463 \log (-6 x-4)-109375 \log (-2 (x+1))+4912 \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 )^3} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.40, size = 146, normalized size = 1.55 \begin {gather*} \frac {1165140 \, x^{4} + 4697400 \, x^{3} + 6842995 \, x^{2} + 208926 \, {\left (18 \, x^{5} + 87 \, x^{4} + 164 \, x^{3} + 151 \, x^{2} + 68 \, x + 12\right )} \log \left (3 \, x + 2\right ) + 9824 \, {\left (18 \, x^{5} + 87 \, x^{4} + 164 \, x^{3} + 151 \, x^{2} + 68 \, x + 12\right )} \log \left (2 \, x + 3\right ) - 218750 \, {\left (18 \, x^{5} + 87 \, x^{4} + 164 \, x^{3} + 151 \, x^{2} + 68 \, x + 12\right )} \log \left (x + 1\right ) + 4275600 \, x + 968615}{1250 \, {\left (18 \, x^{5} + 87 \, x^{4} + 164 \, x^{3} + 151 \, x^{2} + 68 \, x + 12\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 95, normalized size = 1.01 \begin {gather*} -\frac {208}{125 \, {\left (2 \, x + 3\right )}} - \frac {2 \, {\left (\frac {168231}{2 \, x + 3} - \frac {211036}{{\left (2 \, x + 3\right )}^{2}} + \frac {82447}{{\left (2 \, x + 3\right )}^{3}} - 42642\right )}}{125 \, {\left (\frac {5}{2 \, x + 3} - 3\right )}^{2} {\left (\frac {1}{2 \, x + 3} - 1\right )}^{2}} - 175 \, \log \left ({\left | -\frac {1}{2 \, x + 3} + 1 \right |}\right ) + \frac {104463}{625} \, \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 = 0.05, size = 65, normalized size = 0.69 \begin {gather*} \frac {104463 \ln \left (3 x +2\right )}{625}+\frac {4912 \ln \left (2 x +3\right )}{625}-175 \ln \left (x +1\right )-\frac {459}{50 \left (3 x +2\right )^{2}}+\frac {8856}{125 \left (3 x +2\right )}-\frac {208}{125 \left (2 x +3\right )}+\frac {3}{\left (x +1\right )^{2}}+\frac {29}{x +1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.69, size = 72, normalized size = 0.77 \begin {gather*} \frac {233028 \, x^{4} + 939480 \, x^{3} + 1368599 \, x^{2} + 855120 \, x + 193723}{250 \, {\left (18 \, x^{5} + 87 \, x^{4} + 164 \, x^{3} + 151 \, x^{2} + 68 \, x + 12\right )}} + \frac {104463}{625} \, \log \left (3 \, x + 2\right ) + \frac {4912}{625} \, \log \left (2 \, x + 3\right ) - 175 \, \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 = 65, normalized size = 0.69 \begin {gather*} \frac {104463\,\ln \left (x+\frac {2}{3}\right )}{625}-175\,\ln \left (x+1\right )+\frac {4912\,\ln \left (x+\frac {3}{2}\right )}{625}+\frac {\frac {6473\,x^4}{125}+\frac {15658\,x^3}{75}+\frac {1368599\,x^2}{4500}+\frac {14252\,x}{75}+\frac {193723}{4500}}{x^5+\frac {29\,x^4}{6}+\frac {82\,x^3}{9}+\frac {151\,x^2}{18}+\frac {34\,x}{9}+\frac {2}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.23, size = 73, normalized size = 0.78 \begin {gather*} - \frac {- 233028 x^{4} - 939480 x^{3} - 1368599 x^{2} - 855120 x - 193723}{4500 x^{5} + 21750 x^{4} + 41000 x^{3} + 37750 x^{2} + 17000 x + 3000} + \frac {104463 \log {\left (x + \frac {2}{3} \right )}}{625} - 175 \log {\left (x + 1 \right )} + \frac {4912 \log {\left (x + \frac {3}{2} \right )}}{625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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