Optimal. Leaf size=98 \[ -\frac{10648}{823543 (3 x+2)}-\frac{2662}{117649 (3 x+2)^2}-\frac{2662}{50421 (3 x+2)^3}-\frac{1331}{9604 (3 x+2)^4}+\frac{3469}{46305 (3 x+2)^5}-\frac{103}{7938 (3 x+2)^6}+\frac{1}{1323 (3 x+2)^7}-\frac{21296 \log (1-2 x)}{5764801}+\frac{21296 \log (3 x+2)}{5764801} \]
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Rubi [A] time = 0.0361192, antiderivative size = 98, 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} \[ -\frac{10648}{823543 (3 x+2)}-\frac{2662}{117649 (3 x+2)^2}-\frac{2662}{50421 (3 x+2)^3}-\frac{1331}{9604 (3 x+2)^4}+\frac{3469}{46305 (3 x+2)^5}-\frac{103}{7938 (3 x+2)^6}+\frac{1}{1323 (3 x+2)^7}-\frac{21296 \log (1-2 x)}{5764801}+\frac{21296 \log (3 x+2)}{5764801} \]
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)^8} \, dx &=\int \left (-\frac{42592}{5764801 (-1+2 x)}-\frac{1}{63 (2+3 x)^8}+\frac{103}{441 (2+3 x)^7}-\frac{3469}{3087 (2+3 x)^6}+\frac{3993}{2401 (2+3 x)^5}+\frac{7986}{16807 (2+3 x)^4}+\frac{15972}{117649 (2+3 x)^3}+\frac{31944}{823543 (2+3 x)^2}+\frac{63888}{5764801 (2+3 x)}\right ) \, dx\\ &=\frac{1}{1323 (2+3 x)^7}-\frac{103}{7938 (2+3 x)^6}+\frac{3469}{46305 (2+3 x)^5}-\frac{1331}{9604 (2+3 x)^4}-\frac{2662}{50421 (2+3 x)^3}-\frac{2662}{117649 (2+3 x)^2}-\frac{10648}{823543 (2+3 x)}-\frac{21296 \log (1-2 x)}{5764801}+\frac{21296 \log (2+3 x)}{5764801}\\ \end{align*}
Mathematica [A] time = 0.0536195, size = 62, normalized size = 0.63 \[ \frac{4 \left (-\frac{7 \left (12575075040 x^6+57635760600 x^5+113990726520 x^4+127327486275 x^3+83293304778 x^2+29451465714 x+4309941128\right )}{16 (3 x+2)^7}-2156220 \log (1-2 x)+2156220 \log (6 x+4)\right )}{2334744405} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.008, size = 81, normalized size = 0.8 \begin{align*} -{\frac{21296\,\ln \left ( 2\,x-1 \right ) }{5764801}}+{\frac{1}{1323\, \left ( 2+3\,x \right ) ^{7}}}-{\frac{103}{7938\, \left ( 2+3\,x \right ) ^{6}}}+{\frac{3469}{46305\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{1331}{9604\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{2662}{50421\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{2662}{117649\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{10648}{1647086+2470629\,x}}+{\frac{21296\,\ln \left ( 2+3\,x \right ) }{5764801}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06818, size = 116, normalized size = 1.18 \begin{align*} -\frac{12575075040 \, x^{6} + 57635760600 \, x^{5} + 113990726520 \, x^{4} + 127327486275 \, x^{3} + 83293304778 \, x^{2} + 29451465714 \, x + 4309941128}{1334139660 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} + \frac{21296}{5764801} \, \log \left (3 \, x + 2\right ) - \frac{21296}{5764801} \, \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 = 1.23788, size = 598, normalized size = 6.1 \begin{align*} -\frac{88025525280 \, x^{6} + 403450324200 \, x^{5} + 797935085640 \, x^{4} + 891292403925 \, x^{3} + 583053133446 \, x^{2} - 34499520 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )} \log \left (3 \, x + 2\right ) + 34499520 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )} \log \left (2 \, x - 1\right ) + 206160259998 \, x + 30169587896}{9338977620 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.228434, size = 85, normalized size = 0.87 \begin{align*} - \frac{12575075040 x^{6} + 57635760600 x^{5} + 113990726520 x^{4} + 127327486275 x^{3} + 83293304778 x^{2} + 29451465714 x + 4309941128}{2917763436420 x^{7} + 13616229369960 x^{6} + 27232458739920 x^{5} + 30258287488800 x^{4} + 20172191659200 x^{3} + 8068876663680 x^{2} + 1793083703040 x + 170769876480} - \frac{21296 \log{\left (x - \frac{1}{2} \right )}}{5764801} + \frac{21296 \log{\left (x + \frac{2}{3} \right )}}{5764801} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.69947, size = 78, normalized size = 0.8 \begin{align*} -\frac{12575075040 \, x^{6} + 57635760600 \, x^{5} + 113990726520 \, x^{4} + 127327486275 \, x^{3} + 83293304778 \, x^{2} + 29451465714 \, x + 4309941128}{1334139660 \,{\left (3 \, x + 2\right )}^{7}} + \frac{21296}{5764801} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac{21296}{5764801} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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