Optimal. Leaf size=87 \[ -\frac{5324}{117649 (3 x+2)}-\frac{1331}{16807 (3 x+2)^2}-\frac{1331}{7203 (3 x+2)^3}+\frac{3469}{37044 (3 x+2)^4}-\frac{103}{6615 (3 x+2)^5}+\frac{1}{1134 (3 x+2)^6}-\frac{10648 \log (1-2 x)}{823543}+\frac{10648 \log (3 x+2)}{823543} \]
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Rubi [A] time = 0.0327222, antiderivative size = 87, 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} \[ -\frac{5324}{117649 (3 x+2)}-\frac{1331}{16807 (3 x+2)^2}-\frac{1331}{7203 (3 x+2)^3}+\frac{3469}{37044 (3 x+2)^4}-\frac{103}{6615 (3 x+2)^5}+\frac{1}{1134 (3 x+2)^6}-\frac{10648 \log (1-2 x)}{823543}+\frac{10648 \log (3 x+2)}{823543} \]
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)^7} \, dx &=\int \left (-\frac{21296}{823543 (-1+2 x)}-\frac{1}{63 (2+3 x)^7}+\frac{103}{441 (2+3 x)^6}-\frac{3469}{3087 (2+3 x)^5}+\frac{3993}{2401 (2+3 x)^4}+\frac{7986}{16807 (2+3 x)^3}+\frac{15972}{117649 (2+3 x)^2}+\frac{31944}{823543 (2+3 x)}\right ) \, dx\\ &=\frac{1}{1134 (2+3 x)^6}-\frac{103}{6615 (2+3 x)^5}+\frac{3469}{37044 (2+3 x)^4}-\frac{1331}{7203 (2+3 x)^3}-\frac{1331}{16807 (2+3 x)^2}-\frac{5324}{117649 (2+3 x)}-\frac{10648 \log (1-2 x)}{823543}+\frac{10648 \log (2+3 x)}{823543}\\ \end{align*}
Mathematica [A] time = 0.0403115, size = 57, normalized size = 0.66 \[ \frac{4 \left (-\frac{7 \left (2095845840 x^5+8208729540 x^4+13525968060 x^3+11211272235 x^2+4581535248 x+733614062\right )}{16 (3 x+2)^6}-1078110 \log (1-2 x)+1078110 \log (6 x+4)\right )}{333534915} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 72, normalized size = 0.8 \begin{align*} -{\frac{10648\,\ln \left ( 2\,x-1 \right ) }{823543}}+{\frac{1}{1134\, \left ( 2+3\,x \right ) ^{6}}}-{\frac{103}{6615\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{3469}{37044\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{1331}{7203\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{1331}{16807\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{5324}{235298+352947\,x}}+{\frac{10648\,\ln \left ( 2+3\,x \right ) }{823543}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.12494, size = 103, normalized size = 1.18 \begin{align*} -\frac{2095845840 \, x^{5} + 8208729540 \, x^{4} + 13525968060 \, x^{3} + 11211272235 \, x^{2} + 4581535248 \, x + 733614062}{190591380 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} + \frac{10648}{823543} \, \log \left (3 \, x + 2\right ) - \frac{10648}{823543} \, \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 = 1.23359, size = 493, normalized size = 5.67 \begin{align*} -\frac{14670920880 \, x^{5} + 57461106780 \, x^{4} + 94681776420 \, x^{3} + 78478905645 \, x^{2} - 17249760 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (3 \, x + 2\right ) + 17249760 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (2 \, x - 1\right ) + 32070746736 \, x + 5135298434}{1334139660 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.207771, size = 75, normalized size = 0.86 \begin{align*} - \frac{2095845840 x^{5} + 8208729540 x^{4} + 13525968060 x^{3} + 11211272235 x^{2} + 4581535248 x + 733614062}{138941116020 x^{6} + 555764464080 x^{5} + 926274106800 x^{4} + 823354761600 x^{3} + 411677380800 x^{2} + 109780634880 x + 12197848320} - \frac{10648 \log{\left (x - \frac{1}{2} \right )}}{823543} + \frac{10648 \log{\left (x + \frac{2}{3} \right )}}{823543} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.42019, size = 72, normalized size = 0.83 \begin{align*} -\frac{2095845840 \, x^{5} + 8208729540 \, x^{4} + 13525968060 \, x^{3} + 11211272235 \, x^{2} + 4581535248 \, x + 733614062}{190591380 \,{\left (3 \, x + 2\right )}^{6}} + \frac{10648}{823543} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac{10648}{823543} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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