Optimal. Leaf size=87 \[ \frac {5324}{117649 (1-2 x)}-\frac {14520}{117649 (3 x+2)}-\frac {3267}{33614 (3 x+2)^2}+\frac {121}{2401 (3 x+2)^3}-\frac {101}{12348 (3 x+2)^4}+\frac {1}{2205 (3 x+2)^5}-\frac {45012 \log (1-2 x)}{823543}+\frac {45012 \log (3 x+2)}{823543} \]
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Rubi [A] time = 0.04, antiderivative size = 87, normalized size of antiderivative = 1.00, 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} \[ \frac {5324}{117649 (1-2 x)}-\frac {14520}{117649 (3 x+2)}-\frac {3267}{33614 (3 x+2)^2}+\frac {121}{2401 (3 x+2)^3}-\frac {101}{12348 (3 x+2)^4}+\frac {1}{2205 (3 x+2)^5}-\frac {45012 \log (1-2 x)}{823543}+\frac {45012 \log (3 x+2)}{823543} \]
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)^6} \, dx &=\int \left (\frac {10648}{117649 (-1+2 x)^2}-\frac {90024}{823543 (-1+2 x)}-\frac {1}{147 (2+3 x)^6}+\frac {101}{1029 (2+3 x)^5}-\frac {1089}{2401 (2+3 x)^4}+\frac {9801}{16807 (2+3 x)^3}+\frac {43560}{117649 (2+3 x)^2}+\frac {135036}{823543 (2+3 x)}\right ) \, dx\\ &=\frac {5324}{117649 (1-2 x)}+\frac {1}{2205 (2+3 x)^5}-\frac {101}{12348 (2+3 x)^4}+\frac {121}{2401 (2+3 x)^3}-\frac {3267}{33614 (2+3 x)^2}-\frac {14520}{117649 (2+3 x)}-\frac {45012 \log (1-2 x)}{823543}+\frac {45012 \log (2+3 x)}{823543}\\ \end {align*}
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Mathematica [A] time = 0.11, size = 64, normalized size = 0.74 \[ \frac {2 \left (-\frac {7 \left (656274960 x^5+1804756140 x^4+1747028250 x^3+649342770 x^2+25985087 x-23684986\right )}{8 (2 x-1) (3 x+2)^5}-1012770 \log (1-2 x)+1012770 \log (6 x+4)\right )}{37059435} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.74, size = 135, normalized size = 1.55 \[ -\frac {4593924720 \, x^{5} + 12633292980 \, x^{4} + 12229197750 \, x^{3} + 4545399390 \, x^{2} - 8102160 \, {\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )} \log \left (3 \, x + 2\right ) + 8102160 \, {\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )} \log \left (2 \, x - 1\right ) + 181895609 \, x - 165794902}{148237740 \, {\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.96, size = 78, normalized size = 0.90 \[ -\frac {5324}{117649 \, {\left (2 \, x - 1\right )}} + \frac {2 \, {\left (\frac {204418935}{2 \, x - 1} + \frac {740244225}{{\left (2 \, x - 1\right )}^{2}} + \frac {1185622375}{{\left (2 \, x - 1\right )}^{3}} + \frac {709135350}{{\left (2 \, x - 1\right )}^{4}} + 21049983\right )}}{4117715 \, {\left (\frac {7}{2 \, x - 1} + 3\right )}^{5}} + \frac {45012}{823543} \, \log \left ({\left | -\frac {7}{2 \, x - 1} - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 72, normalized size = 0.83 \[ -\frac {45012 \ln \left (2 x -1\right )}{823543}+\frac {45012 \ln \left (3 x +2\right )}{823543}+\frac {1}{2205 \left (3 x +2\right )^{5}}-\frac {101}{12348 \left (3 x +2\right )^{4}}+\frac {121}{2401 \left (3 x +2\right )^{3}}-\frac {3267}{33614 \left (3 x +2\right )^{2}}-\frac {14520}{117649 \left (3 x +2\right )}-\frac {5324}{117649 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 76, normalized size = 0.87 \[ -\frac {656274960 \, x^{5} + 1804756140 \, x^{4} + 1747028250 \, x^{3} + 649342770 \, x^{2} + 25985087 \, x - 23684986}{21176820 \, {\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )}} + \frac {45012}{823543} \, \log \left (3 \, x + 2\right ) - \frac {45012}{823543} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 66, normalized size = 0.76 \[ \frac {90024\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{823543}-\frac {\frac {7502\,x^5}{117649}+\frac {41261\,x^4}{235298}+\frac {2156825\,x^3}{12706092}+\frac {21644759\,x^2}{343064484}+\frac {25985087\,x}{10291934520}-\frac {11842493}{5145967260}}{x^6+\frac {17\,x^5}{6}+\frac {25\,x^4}{9}+\frac {20\,x^3}{27}-\frac {40\,x^2}{81}-\frac {88\,x}{243}-\frac {16}{243}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 75, normalized size = 0.86 \[ \frac {- 656274960 x^{5} - 1804756140 x^{4} - 1747028250 x^{3} - 649342770 x^{2} - 25985087 x + 23684986}{10291934520 x^{6} + 29160481140 x^{5} + 28588707000 x^{4} + 7623655200 x^{3} - 5082436800 x^{2} - 3727120320 x - 677658240} - \frac {45012 \log {\left (x - \frac {1}{2} \right )}}{823543} + \frac {45012 \log {\left (x + \frac {2}{3} \right )}}{823543} \]
Verification of antiderivative is not currently implemented for this CAS.
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