Optimal. Leaf size=87 \[ \frac{14520}{117649 (1-2 x)}-\frac{7755}{117649 (3 x+2)}+\frac{1331}{16807 (1-2 x)^2}+\frac{1023}{33614 (3 x+2)^2}-\frac{11}{2401 (3 x+2)^3}+\frac{1}{4116 (3 x+2)^4}-\frac{59070 \log (1-2 x)}{823543}+\frac{59070 \log (3 x+2)}{823543} \]
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Rubi [A] time = 0.044184, 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} \[ \frac{14520}{117649 (1-2 x)}-\frac{7755}{117649 (3 x+2)}+\frac{1331}{16807 (1-2 x)^2}+\frac{1023}{33614 (3 x+2)^2}-\frac{11}{2401 (3 x+2)^3}+\frac{1}{4116 (3 x+2)^4}-\frac{59070 \log (1-2 x)}{823543}+\frac{59070 \log (3 x+2)}{823543} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(3+5 x)^3}{(1-2 x)^3 (2+3 x)^5} \, dx &=\int \left (-\frac{5324}{16807 (-1+2 x)^3}+\frac{29040}{117649 (-1+2 x)^2}-\frac{118140}{823543 (-1+2 x)}-\frac{1}{343 (2+3 x)^5}+\frac{99}{2401 (2+3 x)^4}-\frac{3069}{16807 (2+3 x)^3}+\frac{23265}{117649 (2+3 x)^2}+\frac{177210}{823543 (2+3 x)}\right ) \, dx\\ &=\frac{1331}{16807 (1-2 x)^2}+\frac{14520}{117649 (1-2 x)}+\frac{1}{4116 (2+3 x)^4}-\frac{11}{2401 (2+3 x)^3}+\frac{1023}{33614 (2+3 x)^2}-\frac{7755}{117649 (2+3 x)}-\frac{59070 \log (1-2 x)}{823543}+\frac{59070 \log (2+3 x)}{823543}\\ \end{align*}
Mathematica [A] time = 0.0505815, size = 64, normalized size = 0.74 \[ \frac{-\frac{7 \left (38277360 x^5+60605820 x^4+8860500 x^3-32767930 x^2-21371408 x-3991495\right )}{4 (1-2 x)^2 (3 x+2)^4}-177210 \log (1-2 x)+177210 \log (6 x+4)}{2470629} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 72, normalized size = 0.8 \begin{align*}{\frac{1331}{16807\, \left ( 2\,x-1 \right ) ^{2}}}-{\frac{14520}{235298\,x-117649}}-{\frac{59070\,\ln \left ( 2\,x-1 \right ) }{823543}}+{\frac{1}{4116\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{11}{2401\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{1023}{33614\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{7755}{235298+352947\,x}}+{\frac{59070\,\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 = 2.44126, size = 103, normalized size = 1.18 \begin{align*} -\frac{38277360 \, x^{5} + 60605820 \, x^{4} + 8860500 \, x^{3} - 32767930 \, x^{2} - 21371408 \, x - 3991495}{1411788 \,{\left (324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right )}} + \frac{59070}{823543} \, \log \left (3 \, x + 2\right ) - \frac{59070}{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 = 1.77733, size = 441, normalized size = 5.07 \begin{align*} -\frac{267941520 \, x^{5} + 424240740 \, x^{4} + 62023500 \, x^{3} - 229375510 \, x^{2} - 708840 \,{\left (324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right )} \log \left (3 \, x + 2\right ) + 708840 \,{\left (324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right )} \log \left (2 \, x - 1\right ) - 149599856 \, x - 27940465}{9882516 \,{\left (324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.208653, size = 75, normalized size = 0.86 \begin{align*} - \frac{38277360 x^{5} + 60605820 x^{4} + 8860500 x^{3} - 32767930 x^{2} - 21371408 x - 3991495}{457419312 x^{6} + 762365520 x^{5} + 114354828 x^{4} - 372712032 x^{3} - 146825952 x^{2} + 45177216 x + 22588608} - \frac{59070 \log{\left (x - \frac{1}{2} \right )}}{823543} + \frac{59070 \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 = 1.97344, size = 105, normalized size = 1.21 \begin{align*} -\frac{7755}{117649 \,{\left (3 \, x + 2\right )}} + \frac{4356 \,{\left (\frac{217}{3 \, x + 2} - 51\right )}}{823543 \,{\left (\frac{7}{3 \, x + 2} - 2\right )}^{2}} + \frac{1023}{33614 \,{\left (3 \, x + 2\right )}^{2}} - \frac{11}{2401 \,{\left (3 \, x + 2\right )}^{3}} + \frac{1}{4116 \,{\left (3 \, x + 2\right )}^{4}} - \frac{59070}{823543} \, \log \left ({\left | -\frac{7}{3 \, x + 2} + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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