Integrand size = 22, antiderivative size = 98 \[ \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^7} \, dx=\frac {10648}{823543 (1-2 x)}+\frac {1}{2646 (2+3 x)^6}-\frac {101}{15435 (2+3 x)^5}+\frac {363}{9604 (2+3 x)^4}-\frac {1089}{16807 (2+3 x)^3}-\frac {7260}{117649 (2+3 x)^2}-\frac {45012}{823543 (2+3 x)}-\frac {17424 \log (1-2 x)}{823543}+\frac {17424 \log (2+3 x)}{823543} \]
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Time = 0.04 (sec) , antiderivative size = 98, 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} \[ \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^7} \, dx=\frac {10648}{823543 (1-2 x)}-\frac {45012}{823543 (3 x+2)}-\frac {7260}{117649 (3 x+2)^2}-\frac {1089}{16807 (3 x+2)^3}+\frac {363}{9604 (3 x+2)^4}-\frac {101}{15435 (3 x+2)^5}+\frac {1}{2646 (3 x+2)^6}-\frac {17424 \log (1-2 x)}{823543}+\frac {17424 \log (3 x+2)}{823543} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \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*}
Time = 0.07 (sec) , antiderivative size = 69, normalized size of antiderivative = 0.70 \[ \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^7} \, dx=\frac {4 \left (-\frac {7 \left (-145404842-461259404 x+887377581 x^2+5935583610 x^3+10278112680 x^4+7811789040 x^5+2286377280 x^6\right )}{16 (-1+2 x) (2+3 x)^6}-588060 \log (1-2 x)+588060 \log (4+6 x)\right )}{111178305} \]
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Time = 2.69 (sec) , antiderivative size = 63, normalized size of antiderivative = 0.64
method | result | size |
norman | \(\frac {-\frac {98597509}{7058940} x^{2}-\frac {19033542}{117649} x^{4}-\frac {14466276}{117649} x^{5}-\frac {4234032}{117649} x^{6}+\frac {115314851}{15882615} x -\frac {21983643}{235298} x^{3}+\frac {72702421}{31765230}}{\left (-1+2 x \right ) \left (2+3 x \right )^{6}}-\frac {17424 \ln \left (-1+2 x \right )}{823543}+\frac {17424 \ln \left (2+3 x \right )}{823543}\) | \(63\) |
risch | \(\frac {-\frac {98597509}{7058940} x^{2}-\frac {19033542}{117649} x^{4}-\frac {14466276}{117649} x^{5}-\frac {4234032}{117649} x^{6}+\frac {115314851}{15882615} x -\frac {21983643}{235298} x^{3}+\frac {72702421}{31765230}}{\left (-1+2 x \right ) \left (2+3 x \right )^{6}}-\frac {17424 \ln \left (-1+2 x \right )}{823543}+\frac {17424 \ln \left (2+3 x \right )}{823543}\) | \(64\) |
default | \(-\frac {10648}{823543 \left (-1+2 x \right )}-\frac {17424 \ln \left (-1+2 x \right )}{823543}+\frac {1}{2646 \left (2+3 x \right )^{6}}-\frac {101}{15435 \left (2+3 x \right )^{5}}+\frac {363}{9604 \left (2+3 x \right )^{4}}-\frac {1089}{16807 \left (2+3 x \right )^{3}}-\frac {7260}{117649 \left (2+3 x \right )^{2}}-\frac {45012}{823543 \left (2+3 x \right )}+\frac {17424 \ln \left (2+3 x \right )}{823543}\) | \(81\) |
parallelrisch | \(\frac {-4617506880 x -11240570880 \ln \left (\frac {2}{3}+x \right ) x^{2}-4995809280 \ln \left (\frac {2}{3}+x \right ) x +63438154164 x^{5}+77216839623 x^{6}+27481515138 x^{7}-49243360320 x^{3}-14021895580 x^{4}-26361513360 x^{2}-42152140800 \ln \left (x -\frac {1}{2}\right ) x^{4}+42152140800 \ln \left (\frac {2}{3}+x \right ) x^{4}-713687040 \ln \left (\frac {2}{3}+x \right )+16258682880 \ln \left (\frac {2}{3}+x \right ) x^{7}+11240570880 \ln \left (x -\frac {1}{2}\right ) x^{2}+4995809280 \ln \left (x -\frac {1}{2}\right ) x +75873853440 \ln \left (\frac {2}{3}+x \right ) x^{5}+56905390080 \ln \left (\frac {2}{3}+x \right ) x^{6}+713687040 \ln \left (x -\frac {1}{2}\right )-16258682880 \ln \left (x -\frac {1}{2}\right ) x^{7}-56905390080 \ln \left (x -\frac {1}{2}\right ) x^{6}-75873853440 \ln \left (x -\frac {1}{2}\right ) x^{5}}{527067520 \left (-1+2 x \right ) \left (2+3 x \right )^{6}}\) | \(167\) |
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Time = 0.22 (sec) , antiderivative size = 140, normalized size of antiderivative = 1.43 \[ \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^7} \, dx=-\frac {16004640960 \, x^{6} + 54682523280 \, x^{5} + 71946788760 \, x^{4} + 41549085270 \, x^{3} + 6211643067 \, x^{2} - 9408960 \, {\left (1458 \, x^{7} + 5103 \, x^{6} + 6804 \, x^{5} + 3780 \, x^{4} - 1008 \, x^{2} - 448 \, x - 64\right )} \log \left (3 \, x + 2\right ) + 9408960 \, {\left (1458 \, x^{7} + 5103 \, x^{6} + 6804 \, x^{5} + 3780 \, x^{4} - 1008 \, x^{2} - 448 \, x - 64\right )} \log \left (2 \, x - 1\right ) - 3228815828 \, x - 1017833894}{444713220 \, {\left (1458 \, x^{7} + 5103 \, x^{6} + 6804 \, x^{5} + 3780 \, x^{4} - 1008 \, x^{2} - 448 \, x - 64\right )}} \]
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Time = 0.09 (sec) , antiderivative size = 80, normalized size of antiderivative = 0.82 \[ \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^7} \, dx=\frac {- 2286377280 x^{6} - 7811789040 x^{5} - 10278112680 x^{4} - 5935583610 x^{3} - 887377581 x^{2} + 461259404 x + 145404842}{92627410680 x^{7} + 324195937380 x^{6} + 432261249840 x^{5} + 240145138800 x^{4} - 64038703680 x^{2} - 28461646080 x - 4065949440} - \frac {17424 \log {\left (x - \frac {1}{2} \right )}}{823543} + \frac {17424 \log {\left (x + \frac {2}{3} \right )}}{823543} \]
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Time = 0.20 (sec) , antiderivative size = 81, normalized size of antiderivative = 0.83 \[ \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^7} \, dx=-\frac {2286377280 \, x^{6} + 7811789040 \, x^{5} + 10278112680 \, x^{4} + 5935583610 \, x^{3} + 887377581 \, x^{2} - 461259404 \, x - 145404842}{63530460 \, {\left (1458 \, x^{7} + 5103 \, x^{6} + 6804 \, x^{5} + 3780 \, x^{4} - 1008 \, x^{2} - 448 \, x - 64\right )}} + \frac {17424}{823543} \, \log \left (3 \, x + 2\right ) - \frac {17424}{823543} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.28 (sec) , antiderivative size = 87, normalized size of antiderivative = 0.89 \[ \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^7} \, dx=-\frac {10648}{823543 \, {\left (2 \, x - 1\right )}} + \frac {4 \, {\left (\frac {1421066052}{2 \, x - 1} + \frac {7028898345}{{\left (2 \, x - 1\right )}^{2}} + \frac {17396565550}{{\left (2 \, x - 1\right )}^{3}} + \frac {21521363500}{{\left (2 \, x - 1\right )}^{4}} + \frac {10637822580}{{\left (2 \, x - 1\right )}^{5}} + 115177113\right )}}{28824005 \, {\left (\frac {7}{2 \, x - 1} + 3\right )}^{6}} + \frac {17424}{823543} \, \log \left ({\left | -\frac {7}{2 \, x - 1} - 3 \right |}\right ) \]
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Time = 1.48 (sec) , antiderivative size = 71, normalized size of antiderivative = 0.72 \[ \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^7} \, dx=\frac {34848\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{823543}-\frac {\frac {2904\,x^6}{117649}+\frac {9922\,x^5}{117649}+\frac {117491\,x^4}{1058841}+\frac {271403\,x^3}{4235364}+\frac {98597509\,x^2}{10291934520}-\frac {115314851\,x}{23156852670}-\frac {72702421}{46313705340}}{x^7+\frac {7\,x^6}{2}+\frac {14\,x^5}{3}+\frac {70\,x^4}{27}-\frac {56\,x^2}{81}-\frac {224\,x}{729}-\frac {32}{729}} \]
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