Integrand size = 22, antiderivative size = 97 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^5 (3+5 x)^2} \, dx=\frac {64}{2033647 (1-2 x)}-\frac {27}{196 (2+3 x)^4}-\frac {666}{343 (2+3 x)^3}-\frac {107109}{4802 (2+3 x)^2}-\frac {5050944}{16807 (2+3 x)}-\frac {15625}{121 (3+5 x)}-\frac {15040 \log (1-2 x)}{156590819}+\frac {222359715 \log (2+3 x)}{117649}-\frac {2515625 \log (3+5 x)}{1331} \]
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Time = 0.04 (sec) , antiderivative size = 97, 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} \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^5 (3+5 x)^2} \, dx=\frac {64}{2033647 (1-2 x)}-\frac {5050944}{16807 (3 x+2)}-\frac {15625}{121 (5 x+3)}-\frac {107109}{4802 (3 x+2)^2}-\frac {666}{343 (3 x+2)^3}-\frac {27}{196 (3 x+2)^4}-\frac {15040 \log (1-2 x)}{156590819}+\frac {222359715 \log (3 x+2)}{117649}-\frac {2515625 \log (5 x+3)}{1331} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {128}{2033647 (-1+2 x)^2}-\frac {30080}{156590819 (-1+2 x)}+\frac {81}{49 (2+3 x)^5}+\frac {5994}{343 (2+3 x)^4}+\frac {321327}{2401 (2+3 x)^3}+\frac {15152832}{16807 (2+3 x)^2}+\frac {667079145}{117649 (2+3 x)}+\frac {78125}{121 (3+5 x)^2}-\frac {12578125}{1331 (3+5 x)}\right ) \, dx \\ & = \frac {64}{2033647 (1-2 x)}-\frac {27}{196 (2+3 x)^4}-\frac {666}{343 (2+3 x)^3}-\frac {107109}{4802 (2+3 x)^2}-\frac {5050944}{16807 (2+3 x)}-\frac {15625}{121 (3+5 x)}-\frac {15040 \log (1-2 x)}{156590819}+\frac {222359715 \log (2+3 x)}{117649}-\frac {2515625 \log (3+5 x)}{1331} \\ \end{align*}
Time = 0.09 (sec) , antiderivative size = 75, normalized size of antiderivative = 0.77 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^5 (3+5 x)^2} \, dx=\frac {-\frac {77 \left (-77754195847-317609203475 x-132753874800 x^2+1064845635750 x^3+1771154199360 x^4+830228340600 x^5\right )}{(2+3 x)^4 \left (-3+x+10 x^2\right )}-60160 \log (3-6 x)+1183843122660 \log (2+3 x)-1183843062500 \log (-3 (3+5 x))}{626363276} \]
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Time = 2.72 (sec) , antiderivative size = 73, normalized size of antiderivative = 0.75
method | result | size |
norman | \(\frac {-\frac {532422817875}{4067294} x^{3}-\frac {207557085150}{2033647} x^{5}-\frac {63255507120}{290521} x^{4}+\frac {33188468700}{2033647} x^{2}+\frac {317609203475}{8134588} x +\frac {77754195847}{8134588}}{\left (-1+2 x \right ) \left (2+3 x \right )^{4} \left (3+5 x \right )}-\frac {15040 \ln \left (-1+2 x \right )}{156590819}+\frac {222359715 \ln \left (2+3 x \right )}{117649}-\frac {2515625 \ln \left (3+5 x \right )}{1331}\) | \(73\) |
risch | \(\frac {-\frac {532422817875}{4067294} x^{3}-\frac {207557085150}{2033647} x^{5}-\frac {63255507120}{290521} x^{4}+\frac {33188468700}{2033647} x^{2}+\frac {317609203475}{8134588} x +\frac {77754195847}{8134588}}{\left (-1+2 x \right ) \left (2+3 x \right )^{4} \left (3+5 x \right )}-\frac {15040 \ln \left (-1+2 x \right )}{156590819}+\frac {222359715 \ln \left (2+3 x \right )}{117649}-\frac {2515625 \ln \left (3+5 x \right )}{1331}\) | \(74\) |
default | \(-\frac {15625}{121 \left (3+5 x \right )}-\frac {2515625 \ln \left (3+5 x \right )}{1331}-\frac {64}{2033647 \left (-1+2 x \right )}-\frac {15040 \ln \left (-1+2 x \right )}{156590819}-\frac {27}{196 \left (2+3 x \right )^{4}}-\frac {666}{343 \left (2+3 x \right )^{3}}-\frac {107109}{4802 \left (2+3 x \right )^{2}}-\frac {5050944}{16807 \left (2+3 x \right )}+\frac {222359715 \ln \left (2+3 x \right )}{117649}\) | \(80\) |
parallelrisch | \(\frac {-454600261775968 x +22275191064000000 \ln \left (x +\frac {3}{5}\right ) x^{2}+30003320100695040 \ln \left (\frac {2}{3}+x \right ) x^{3}+15456255024000000 \ln \left (x +\frac {3}{5}\right ) x -22275192195970560 \ln \left (\frac {2}{3}+x \right ) x^{2}-15456255809448960 \ln \left (\frac {2}{3}+x \right ) x +10348506825913179 x^{5}+4849529194977390 x^{6}-774494883376368 x^{3}+6224240959272567 x^{4}-1856274326185048 x^{2}-6159421440 \ln \left (x -\frac {1}{2}\right ) x^{4}+121206594270421440 \ln \left (\frac {2}{3}+x \right ) x^{4}-2727574554608640 \ln \left (\frac {2}{3}+x \right )-1524695040 \ln \left (x -\frac {1}{2}\right ) x^{3}+1131970560 \ln \left (x -\frac {1}{2}\right ) x^{2}+785448960 \ln \left (x -\frac {1}{2}\right ) x +2727574416000000 \ln \left (x +\frac {3}{5}\right )+127343637018290880 \ln \left (\frac {2}{3}+x \right ) x^{5}-30003318576000000 \ln \left (x +\frac {3}{5}\right ) x^{3}-127343630547000000 \ln \left (x +\frac {3}{5}\right ) x^{5}-121206588111000000 \ln \left (x +\frac {3}{5}\right ) x^{4}+46027820609020800 \ln \left (\frac {2}{3}+x \right ) x^{6}-46027818270000000 \ln \left (x +\frac {3}{5}\right ) x^{6}+138608640 \ln \left (x -\frac {1}{2}\right )-2339020800 \ln \left (x -\frac {1}{2}\right ) x^{6}-6471290880 \ln \left (x -\frac {1}{2}\right ) x^{5}}{30065437248 \left (-1+2 x \right ) \left (2+3 x \right )^{4} \left (3+5 x \right )}\) | \(227\) |
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Leaf count of result is larger than twice the leaf count of optimal. 173 vs. \(2 (79) = 158\).
Time = 0.22 (sec) , antiderivative size = 173, normalized size of antiderivative = 1.78 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^5 (3+5 x)^2} \, dx=-\frac {63927582226200 \, x^{5} + 136378873350720 \, x^{4} + 81993113952750 \, x^{3} - 10222048359600 \, x^{2} + 1183843062500 \, {\left (810 \, x^{6} + 2241 \, x^{5} + 2133 \, x^{4} + 528 \, x^{3} - 392 \, x^{2} - 272 \, x - 48\right )} \log \left (5 \, x + 3\right ) - 1183843122660 \, {\left (810 \, x^{6} + 2241 \, x^{5} + 2133 \, x^{4} + 528 \, x^{3} - 392 \, x^{2} - 272 \, x - 48\right )} \log \left (3 \, x + 2\right ) + 60160 \, {\left (810 \, x^{6} + 2241 \, x^{5} + 2133 \, x^{4} + 528 \, x^{3} - 392 \, x^{2} - 272 \, x - 48\right )} \log \left (2 \, x - 1\right ) - 24455908667575 \, x - 5987073080219}{626363276 \, {\left (810 \, x^{6} + 2241 \, x^{5} + 2133 \, x^{4} + 528 \, x^{3} - 392 \, x^{2} - 272 \, x - 48\right )}} \]
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Time = 0.12 (sec) , antiderivative size = 85, normalized size of antiderivative = 0.88 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^5 (3+5 x)^2} \, dx=\frac {- 830228340600 x^{5} - 1771154199360 x^{4} - 1064845635750 x^{3} + 132753874800 x^{2} + 317609203475 x + 77754195847}{6589016280 x^{6} + 18229611708 x^{5} + 17351076204 x^{4} + 4295062464 x^{3} - 3188758496 x^{2} - 2212607936 x - 390460224} - \frac {15040 \log {\left (x - \frac {1}{2} \right )}}{156590819} - \frac {2515625 \log {\left (x + \frac {3}{5} \right )}}{1331} + \frac {222359715 \log {\left (x + \frac {2}{3} \right )}}{117649} \]
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Time = 0.23 (sec) , antiderivative size = 84, normalized size of antiderivative = 0.87 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^5 (3+5 x)^2} \, dx=-\frac {830228340600 \, x^{5} + 1771154199360 \, x^{4} + 1064845635750 \, x^{3} - 132753874800 \, x^{2} - 317609203475 \, x - 77754195847}{8134588 \, {\left (810 \, x^{6} + 2241 \, x^{5} + 2133 \, x^{4} + 528 \, x^{3} - 392 \, x^{2} - 272 \, x - 48\right )}} - \frac {2515625}{1331} \, \log \left (5 \, x + 3\right ) + \frac {222359715}{117649} \, \log \left (3 \, x + 2\right ) - \frac {15040}{156590819} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.28 (sec) , antiderivative size = 104, normalized size of antiderivative = 1.07 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^5 (3+5 x)^2} \, dx=-\frac {15625}{121 \, {\left (5 \, x + 3\right )}} + \frac {25 \, {\left (\frac {6062344264539}{5 \, x + 3} + \frac {7964082495612}{{\left (5 \, x + 3\right )}^{2}} + \frac {3205106234076}{{\left (5 \, x + 3\right )}^{3}} + \frac {435889532968}{{\left (5 \, x + 3\right )}^{4}} - 1385260555122\right )}}{89480468 \, {\left (\frac {11}{5 \, x + 3} - 2\right )} {\left (\frac {1}{5 \, x + 3} + 3\right )}^{4}} + \frac {222359715}{117649} \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) - \frac {15040}{156590819} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) \]
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Time = 1.22 (sec) , antiderivative size = 75, normalized size of antiderivative = 0.77 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^5 (3+5 x)^2} \, dx=\frac {222359715\,\ln \left (x+\frac {2}{3}\right )}{117649}-\frac {15040\,\ln \left (x-\frac {1}{2}\right )}{156590819}-\frac {2515625\,\ln \left (x+\frac {3}{5}\right )}{1331}+\frac {-\frac {256243315\,x^5}{2033647}-\frac {234279656\,x^4}{871563}-\frac {3943872725\,x^3}{24403764}+\frac {1106282290\,x^2}{54908469}+\frac {63521840695\,x}{1317803256}+\frac {77754195847}{6589016280}}{x^6+\frac {83\,x^5}{30}+\frac {79\,x^4}{30}+\frac {88\,x^3}{135}-\frac {196\,x^2}{405}-\frac {136\,x}{405}-\frac {8}{135}} \]
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