Optimal. Leaf size=76 \[ -\frac{2662}{16807 (3 x+2)}-\frac{1331}{4802 (3 x+2)^2}+\frac{3469}{27783 (3 x+2)^3}-\frac{103}{5292 (3 x+2)^4}+\frac{1}{945 (3 x+2)^5}-\frac{5324 \log (1-2 x)}{117649}+\frac{5324 \log (3 x+2)}{117649} \]
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Rubi [A] time = 0.0292861, antiderivative size = 76, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {88} \[ -\frac{2662}{16807 (3 x+2)}-\frac{1331}{4802 (3 x+2)^2}+\frac{3469}{27783 (3 x+2)^3}-\frac{103}{5292 (3 x+2)^4}+\frac{1}{945 (3 x+2)^5}-\frac{5324 \log (1-2 x)}{117649}+\frac{5324 \log (3 x+2)}{117649} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(3+5 x)^3}{(1-2 x) (2+3 x)^6} \, dx &=\int \left (-\frac{10648}{117649 (-1+2 x)}-\frac{1}{63 (2+3 x)^6}+\frac{103}{441 (2+3 x)^5}-\frac{3469}{3087 (2+3 x)^4}+\frac{3993}{2401 (2+3 x)^3}+\frac{7986}{16807 (2+3 x)^2}+\frac{15972}{117649 (2+3 x)}\right ) \, dx\\ &=\frac{1}{945 (2+3 x)^5}-\frac{103}{5292 (2+3 x)^4}+\frac{3469}{27783 (2+3 x)^3}-\frac{1331}{4802 (2+3 x)^2}-\frac{2662}{16807 (2+3 x)}-\frac{5324 \log (1-2 x)}{117649}+\frac{5324 \log (2+3 x)}{117649}\\ \end{align*}
Mathematica [A] time = 0.0436359, size = 52, normalized size = 0.68 \[ \frac{2 \left (-\frac{7 \left (349307640 x^4+1135249830 x^3+1308416040 x^2+646472325 x+116805778\right )}{8 (3 x+2)^5}-1078110 \log (1-2 x)+1078110 \log (6 x+4)\right )}{47647845} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 63, normalized size = 0.8 \begin{align*} -{\frac{5324\,\ln \left ( 2\,x-1 \right ) }{117649}}+{\frac{1}{945\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{103}{5292\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{3469}{27783\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{1331}{4802\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{2662}{33614+50421\,x}}+{\frac{5324\,\ln \left ( 2+3\,x \right ) }{117649}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.21967, size = 89, normalized size = 1.17 \begin{align*} -\frac{349307640 \, x^{4} + 1135249830 \, x^{3} + 1308416040 \, x^{2} + 646472325 \, x + 116805778}{27227340 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} + \frac{5324}{117649} \, \log \left (3 \, x + 2\right ) - \frac{5324}{117649} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.13844, size = 405, normalized size = 5.33 \begin{align*} -\frac{2445153480 \, x^{4} + 7946748810 \, x^{3} + 9158912280 \, x^{2} - 8624880 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (3 \, x + 2\right ) + 8624880 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (2 \, x - 1\right ) + 4525306275 \, x + 817640446}{190591380 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.190415, size = 65, normalized size = 0.86 \begin{align*} - \frac{349307640 x^{4} + 1135249830 x^{3} + 1308416040 x^{2} + 646472325 x + 116805778}{6616243620 x^{5} + 22054145400 x^{4} + 29405527200 x^{3} + 19603684800 x^{2} + 6534561600 x + 871274880} - \frac{5324 \log{\left (x - \frac{1}{2} \right )}}{117649} + \frac{5324 \log{\left (x + \frac{2}{3} \right )}}{117649} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.97159, size = 65, normalized size = 0.86 \begin{align*} -\frac{349307640 \, x^{4} + 1135249830 \, x^{3} + 1308416040 \, x^{2} + 646472325 \, x + 116805778}{27227340 \,{\left (3 \, x + 2\right )}^{5}} + \frac{5324}{117649} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac{5324}{117649} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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