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 = 0.0502562, antiderivative size = 77, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.08, Rules used = {822, 800} \[ -\frac{3 (47 x+37)}{5 (2 x+3)^2 \left (3 x^2+5 x+2\right )}-\frac{2618}{125 (2 x+3)}-\frac{428}{25 (2 x+3)^2}-\log (x+1)+\frac{8104}{625} \log (2 x+3)-\frac{7479}{625} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 822
Rule 800
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*}
Mathematica [A] time = 0.0317155, size = 66, normalized size = 0.86 \[ \frac{1}{625} \left (-\frac{15 (903 x+653)}{3 x^2+5 x+2}-\frac{4060}{2 x+3}-\frac{650}{(2 x+3)^2}-7479 \log (-6 x-4)-625 \log (-2 (x+1))+8104 \log (2 x+3)\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.01, size = 58, normalized size = 0.8 \begin{align*} -6\, \left ( 1+x \right ) ^{-1}-\ln \left ( 1+x \right ) -{\frac{26}{25\, \left ( 3+2\,x \right ) ^{2}}}-{\frac{812}{375+250\,x}}+{\frac{8104\,\ln \left ( 3+2\,x \right ) }{625}}-{\frac{459}{250+375\,x}}-{\frac{7479\,\ln \left ( 2+3\,x \right ) }{625}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01042, size = 84, normalized size = 1.09 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.2591, size = 359, normalized size = 4.66 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.227906, size = 60, normalized size = 0.78 \begin{align*} - \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14908, size = 84, normalized size = 1.09 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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