Optimal. Leaf size=77 \[ -\frac {3 (47 x+37)}{5 (2 x+3)^2 \left (3 x^2+5 x+2\right )}-\frac {2618}{125 (2 x+3)}-\frac {428}{25 (2 x+3)^2}-\log (x+1)+\frac {8104}{625} \log (2 x+3)-\frac {7479}{625} \log (3 x+2) \]
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Rubi [A] time = 0.05, antiderivative size = 77, 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} \begin {gather*} -\frac {3 (47 x+37)}{5 (2 x+3)^2 \left (3 x^2+5 x+2\right )}-\frac {2618}{125 (2 x+3)}-\frac {428}{25 (2 x+3)^2}-\log (x+1)+\frac {8104}{625} \log (2 x+3)-\frac {7479}{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)^3 \left (2+5 x+3 x^2\right )^2} \, dx &=-\frac {3 (37+47 x)}{5 (3+2 x)^2 \left (2+5 x+3 x^2\right )}-\frac {1}{5} \int \frac {841+846 x}{(3+2 x)^3 \left (2+5 x+3 x^2\right )} \, dx\\ &=-\frac {3 (37+47 x)}{5 (3+2 x)^2 \left (2+5 x+3 x^2\right )}-\frac {1}{5} \int \left (\frac {5}{1+x}-\frac {1712}{5 (3+2 x)^3}-\frac {5236}{25 (3+2 x)^2}-\frac {16208}{125 (3+2 x)}+\frac {22437}{125 (2+3 x)}\right ) \, dx\\ &=-\frac {428}{25 (3+2 x)^2}-\frac {2618}{125 (3+2 x)}-\frac {3 (37+47 x)}{5 (3+2 x)^2 \left (2+5 x+3 x^2\right )}-\log (1+x)+\frac {8104}{625} \log (3+2 x)-\frac {7479}{625} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.03, size = 66, normalized size = 0.86 \begin {gather*} \frac {1}{625} \left (-\frac {15 (903 x+653)}{3 x^2+5 x+2}-\frac {4060}{2 x+3}-\frac {650}{(2 x+3)^2}-7479 \log (-6 x-4)-625 \log (-2 (x+1))+8104 \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 )^2} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.39, size = 121, normalized size = 1.57 \begin {gather*} -\frac {78540 \, x^{3} + 280810 \, x^{2} + 7479 \, {\left (12 \, x^{4} + 56 \, x^{3} + 95 \, x^{2} + 69 \, x + 18\right )} \log \left (3 \, x + 2\right ) - 8104 \, {\left (12 \, x^{4} + 56 \, x^{3} + 95 \, x^{2} + 69 \, x + 18\right )} \log \left (2 \, x + 3\right ) + 625 \, {\left (12 \, x^{4} + 56 \, x^{3} + 95 \, x^{2} + 69 \, x + 18\right )} \log \left (x + 1\right ) + 319835 \, x + 113815}{625 \, {\left (12 \, x^{4} + 56 \, x^{3} + 95 \, x^{2} + 69 \, x + 18\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 62, normalized size = 0.81 \begin {gather*} -\frac {15708 \, x^{3} + 56162 \, x^{2} + 63967 \, x + 22763}{125 \, {\left (3 \, x + 2\right )} {\left (2 \, x + 3\right )}^{2} {\left (x + 1\right )}} - \frac {7479}{625} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) + \frac {8104}{625} \, \log \left ({\left | 2 \, x + 3 \right |}\right ) - \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 = 0.06, size = 58, normalized size = 0.75 \begin {gather*} -\frac {7479 \ln \left (3 x +2\right )}{625}+\frac {8104 \ln \left (2 x +3\right )}{625}-\ln \left (x +1\right )-\frac {459}{125 \left (3 x +2\right )}-\frac {26}{25 \left (2 x +3\right )^{2}}-\frac {812}{125 \left (2 x +3\right )}-\frac {6}{x +1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.62, size = 62, normalized size = 0.81 \begin {gather*} -\frac {15708 \, x^{3} + 56162 \, x^{2} + 63967 \, x + 22763}{125 \, {\left (12 \, x^{4} + 56 \, x^{3} + 95 \, x^{2} + 69 \, x + 18\right )}} - \frac {7479}{625} \, \log \left (3 \, x + 2\right ) + \frac {8104}{625} \, \log \left (2 \, x + 3\right ) - \log \left (x + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.31, size = 56, normalized size = 0.73 \begin {gather*} \frac {8104\,\ln \left (x+\frac {3}{2}\right )}{625}-\frac {7479\,\ln \left (x+\frac {2}{3}\right )}{625}-\ln \left (x+1\right )-\frac {\frac {1309\,x^3}{125}+\frac {28081\,x^2}{750}+\frac {63967\,x}{1500}+\frac {22763}{1500}}{x^4+\frac {14\,x^3}{3}+\frac {95\,x^2}{12}+\frac {23\,x}{4}+\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.21, size = 60, normalized size = 0.78 \begin {gather*} - \frac {15708 x^{3} + 56162 x^{2} + 63967 x + 22763}{1500 x^{4} + 7000 x^{3} + 11875 x^{2} + 8625 x + 2250} - \frac {7479 \log {\left (x + \frac {2}{3} \right )}}{625} - \log {\left (x + 1 \right )} + \frac {8104 \log {\left (x + \frac {3}{2} \right )}}{625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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