Optimal. Leaf size=98 \[ \frac{10648}{823543 (1-2 x)}-\frac{45012}{823543 (3 x+2)}-\frac{7260}{117649 (3 x+2)^2}-\frac{1089}{16807 (3 x+2)^3}+\frac{363}{9604 (3 x+2)^4}-\frac{101}{15435 (3 x+2)^5}+\frac{1}{2646 (3 x+2)^6}-\frac{17424 \log (1-2 x)}{823543}+\frac{17424 \log (3 x+2)}{823543} \]
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Rubi [A] time = 0.0501509, 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} \[ \frac{10648}{823543 (1-2 x)}-\frac{45012}{823543 (3 x+2)}-\frac{7260}{117649 (3 x+2)^2}-\frac{1089}{16807 (3 x+2)^3}+\frac{363}{9604 (3 x+2)^4}-\frac{101}{15435 (3 x+2)^5}+\frac{1}{2646 (3 x+2)^6}-\frac{17424 \log (1-2 x)}{823543}+\frac{17424 \log (3 x+2)}{823543} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(3+5 x)^3}{(1-2 x)^2 (2+3 x)^7} \, dx &=\int \left (\frac{21296}{823543 (-1+2 x)^2}-\frac{34848}{823543 (-1+2 x)}-\frac{1}{147 (2+3 x)^7}+\frac{101}{1029 (2+3 x)^6}-\frac{1089}{2401 (2+3 x)^5}+\frac{9801}{16807 (2+3 x)^4}+\frac{43560}{117649 (2+3 x)^3}+\frac{135036}{823543 (2+3 x)^2}+\frac{52272}{823543 (2+3 x)}\right ) \, dx\\ &=\frac{10648}{823543 (1-2 x)}+\frac{1}{2646 (2+3 x)^6}-\frac{101}{15435 (2+3 x)^5}+\frac{363}{9604 (2+3 x)^4}-\frac{1089}{16807 (2+3 x)^3}-\frac{7260}{117649 (2+3 x)^2}-\frac{45012}{823543 (2+3 x)}-\frac{17424 \log (1-2 x)}{823543}+\frac{17424 \log (2+3 x)}{823543}\\ \end{align*}
Mathematica [A] time = 0.0571415, size = 69, normalized size = 0.7 \[ \frac{4 \left (-\frac{7 \left (2286377280 x^6+7811789040 x^5+10278112680 x^4+5935583610 x^3+887377581 x^2-461259404 x-145404842\right )}{16 (2 x-1) (3 x+2)^6}-588060 \log (1-2 x)+588060 \log (6 x+4)\right )}{111178305} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.008, size = 81, normalized size = 0.8 \begin{align*} -{\frac{10648}{1647086\,x-823543}}-{\frac{17424\,\ln \left ( 2\,x-1 \right ) }{823543}}+{\frac{1}{2646\, \left ( 2+3\,x \right ) ^{6}}}-{\frac{101}{15435\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{363}{9604\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{1089}{16807\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{7260}{117649\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{45012}{1647086+2470629\,x}}+{\frac{17424\,\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 = 1.12987, size = 109, normalized size = 1.11 \begin{align*} -\frac{2286377280 \, x^{6} + 7811789040 \, x^{5} + 10278112680 \, x^{4} + 5935583610 \, x^{3} + 887377581 \, x^{2} - 461259404 \, x - 145404842}{63530460 \,{\left (1458 \, x^{7} + 5103 \, x^{6} + 6804 \, x^{5} + 3780 \, x^{4} - 1008 \, x^{2} - 448 \, x - 64\right )}} + \frac{17424}{823543} \, \log \left (3 \, x + 2\right ) - \frac{17424}{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 = 1.31924, size = 514, normalized size = 5.24 \begin{align*} -\frac{16004640960 \, x^{6} + 54682523280 \, x^{5} + 71946788760 \, x^{4} + 41549085270 \, x^{3} + 6211643067 \, x^{2} - 9408960 \,{\left (1458 \, x^{7} + 5103 \, x^{6} + 6804 \, x^{5} + 3780 \, x^{4} - 1008 \, x^{2} - 448 \, x - 64\right )} \log \left (3 \, x + 2\right ) + 9408960 \,{\left (1458 \, x^{7} + 5103 \, x^{6} + 6804 \, x^{5} + 3780 \, x^{4} - 1008 \, x^{2} - 448 \, x - 64\right )} \log \left (2 \, x - 1\right ) - 3228815828 \, x - 1017833894}{444713220 \,{\left (1458 \, x^{7} + 5103 \, x^{6} + 6804 \, x^{5} + 3780 \, x^{4} - 1008 \, x^{2} - 448 \, x - 64\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.206216, size = 80, normalized size = 0.82 \begin{align*} - \frac{2286377280 x^{6} + 7811789040 x^{5} + 10278112680 x^{4} + 5935583610 x^{3} + 887377581 x^{2} - 461259404 x - 145404842}{92627410680 x^{7} + 324195937380 x^{6} + 432261249840 x^{5} + 240145138800 x^{4} - 64038703680 x^{2} - 28461646080 x - 4065949440} - \frac{17424 \log{\left (x - \frac{1}{2} \right )}}{823543} + \frac{17424 \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 = 2.53685, size = 117, normalized size = 1.19 \begin{align*} -\frac{10648}{823543 \,{\left (2 \, x - 1\right )}} + \frac{4 \,{\left (\frac{1421066052}{2 \, x - 1} + \frac{7028898345}{{\left (2 \, x - 1\right )}^{2}} + \frac{17396565550}{{\left (2 \, x - 1\right )}^{3}} + \frac{21521363500}{{\left (2 \, x - 1\right )}^{4}} + \frac{10637822580}{{\left (2 \, x - 1\right )}^{5}} + 115177113\right )}}{28824005 \,{\left (\frac{7}{2 \, x - 1} + 3\right )}^{6}} + \frac{17424}{823543} \, \log \left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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