Integrand size = 22, antiderivative size = 87 \[ \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^6} \, dx=\frac {5324}{117649 (1-2 x)}+\frac {1}{2205 (2+3 x)^5}-\frac {101}{12348 (2+3 x)^4}+\frac {121}{2401 (2+3 x)^3}-\frac {3267}{33614 (2+3 x)^2}-\frac {14520}{117649 (2+3 x)}-\frac {45012 \log (1-2 x)}{823543}+\frac {45012 \log (2+3 x)}{823543} \]
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Time = 0.03 (sec) , antiderivative size = 87, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90} \[ \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^6} \, dx=\frac {5324}{117649 (1-2 x)}-\frac {14520}{117649 (3 x+2)}-\frac {3267}{33614 (3 x+2)^2}+\frac {121}{2401 (3 x+2)^3}-\frac {101}{12348 (3 x+2)^4}+\frac {1}{2205 (3 x+2)^5}-\frac {45012 \log (1-2 x)}{823543}+\frac {45012 \log (3 x+2)}{823543} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \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*}
Time = 0.10 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.74 \[ \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^6} \, dx=\frac {2 \left (-\frac {7 \left (-23684986+25985087 x+649342770 x^2+1747028250 x^3+1804756140 x^4+656274960 x^5\right )}{8 (-1+2 x) (2+3 x)^5}-1012770 \log (1-2 x)+1012770 \log (4+6 x)\right )}{37059435} \]
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Time = 2.70 (sec) , antiderivative size = 58, normalized size of antiderivative = 0.67
method | result | size |
norman | \(\frac {-\frac {25985087}{21176820} x -\frac {21644759}{705894} x^{2}-\frac {19411425}{235298} x^{3}-\frac {10026423}{117649} x^{4}-\frac {3645972}{117649} x^{5}+\frac {11842493}{10588410}}{\left (-1+2 x \right ) \left (2+3 x \right )^{5}}-\frac {45012 \ln \left (-1+2 x \right )}{823543}+\frac {45012 \ln \left (2+3 x \right )}{823543}\) | \(58\) |
risch | \(\frac {-\frac {25985087}{21176820} x -\frac {21644759}{705894} x^{2}-\frac {19411425}{235298} x^{3}-\frac {10026423}{117649} x^{4}-\frac {3645972}{117649} x^{5}+\frac {11842493}{10588410}}{\left (-1+2 x \right ) \left (2+3 x \right )^{5}}-\frac {45012 \ln \left (-1+2 x \right )}{823543}+\frac {45012 \ln \left (2+3 x \right )}{823543}\) | \(59\) |
default | \(-\frac {5324}{117649 \left (-1+2 x \right )}-\frac {45012 \ln \left (-1+2 x \right )}{823543}+\frac {1}{2205 \left (2+3 x \right )^{5}}-\frac {101}{12348 \left (2+3 x \right )^{4}}+\frac {121}{2401 \left (2+3 x \right )^{3}}-\frac {3267}{33614 \left (2+3 x \right )^{2}}-\frac {14520}{117649 \left (2+3 x \right )}+\frac {45012 \ln \left (2+3 x \right )}{823543}\) | \(72\) |
parallelrisch | \(\frac {-1944475680 x +5185382400 \ln \left (\frac {2}{3}+x \right ) x^{3}-3456921600 \ln \left (\frac {2}{3}+x \right ) x^{2}-2535075840 \ln \left (\frac {2}{3}+x \right ) x +4516332723 x^{5}+4476462354 x^{6}-18424897960 x^{3}-10024569870 x^{4}-10291308720 x^{2}-19445184000 \ln \left (x -\frac {1}{2}\right ) x^{4}+19445184000 \ln \left (\frac {2}{3}+x \right ) x^{4}-460922880 \ln \left (\frac {2}{3}+x \right )-5185382400 \ln \left (x -\frac {1}{2}\right ) x^{3}+3456921600 \ln \left (x -\frac {1}{2}\right ) x^{2}+2535075840 \ln \left (x -\frac {1}{2}\right ) x +19834087680 \ln \left (\frac {2}{3}+x \right ) x^{5}+7000266240 \ln \left (\frac {2}{3}+x \right ) x^{6}+460922880 \ln \left (x -\frac {1}{2}\right )-7000266240 \ln \left (x -\frac {1}{2}\right ) x^{6}-19834087680 \ln \left (x -\frac {1}{2}\right ) x^{5}}{263533760 \left (-1+2 x \right ) \left (2+3 x \right )^{5}}\) | \(162\) |
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Time = 0.22 (sec) , antiderivative size = 135, normalized size of antiderivative = 1.55 \[ \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^6} \, dx=-\frac {4593924720 \, x^{5} + 12633292980 \, x^{4} + 12229197750 \, x^{3} + 4545399390 \, x^{2} - 8102160 \, {\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )} \log \left (3 \, x + 2\right ) + 8102160 \, {\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )} \log \left (2 \, x - 1\right ) + 181895609 \, x - 165794902}{148237740 \, {\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )}} \]
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Time = 0.09 (sec) , antiderivative size = 75, normalized size of antiderivative = 0.86 \[ \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^6} \, dx=\frac {- 656274960 x^{5} - 1804756140 x^{4} - 1747028250 x^{3} - 649342770 x^{2} - 25985087 x + 23684986}{10291934520 x^{6} + 29160481140 x^{5} + 28588707000 x^{4} + 7623655200 x^{3} - 5082436800 x^{2} - 3727120320 x - 677658240} - \frac {45012 \log {\left (x - \frac {1}{2} \right )}}{823543} + \frac {45012 \log {\left (x + \frac {2}{3} \right )}}{823543} \]
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Time = 0.21 (sec) , antiderivative size = 76, normalized size of antiderivative = 0.87 \[ \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^6} \, dx=-\frac {656274960 \, x^{5} + 1804756140 \, x^{4} + 1747028250 \, x^{3} + 649342770 \, x^{2} + 25985087 \, x - 23684986}{21176820 \, {\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )}} + \frac {45012}{823543} \, \log \left (3 \, x + 2\right ) - \frac {45012}{823543} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.28 (sec) , antiderivative size = 78, normalized size of antiderivative = 0.90 \[ \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^6} \, dx=-\frac {5324}{117649 \, {\left (2 \, x - 1\right )}} + \frac {2 \, {\left (\frac {204418935}{2 \, x - 1} + \frac {740244225}{{\left (2 \, x - 1\right )}^{2}} + \frac {1185622375}{{\left (2 \, x - 1\right )}^{3}} + \frac {709135350}{{\left (2 \, x - 1\right )}^{4}} + 21049983\right )}}{4117715 \, {\left (\frac {7}{2 \, x - 1} + 3\right )}^{5}} + \frac {45012}{823543} \, \log \left ({\left | -\frac {7}{2 \, x - 1} - 3 \right |}\right ) \]
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Time = 0.05 (sec) , antiderivative size = 66, normalized size of antiderivative = 0.76 \[ \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^6} \, dx=\frac {90024\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{823543}-\frac {\frac {7502\,x^5}{117649}+\frac {41261\,x^4}{235298}+\frac {2156825\,x^3}{12706092}+\frac {21644759\,x^2}{343064484}+\frac {25985087\,x}{10291934520}-\frac {11842493}{5145967260}}{x^6+\frac {17\,x^5}{6}+\frac {25\,x^4}{9}+\frac {20\,x^3}{27}-\frac {40\,x^2}{81}-\frac {88\,x}{243}-\frac {16}{243}} \]
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