Integrand size = 22, antiderivative size = 70 \[ \int \frac {(1-2 x)^3}{(2+3 x)^6 (3+5 x)} \, dx=\frac {343}{135 (2+3 x)^5}+\frac {1421}{108 (2+3 x)^4}+\frac {7189}{81 (2+3 x)^3}+\frac {1331}{2 (2+3 x)^2}+\frac {6655}{2+3 x}-33275 \log (2+3 x)+33275 \log (3+5 x) \]
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Time = 0.02 (sec) , antiderivative size = 70, 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} \[ \int \frac {(1-2 x)^3}{(2+3 x)^6 (3+5 x)} \, dx=\frac {6655}{3 x+2}+\frac {1331}{2 (3 x+2)^2}+\frac {7189}{81 (3 x+2)^3}+\frac {1421}{108 (3 x+2)^4}+\frac {343}{135 (3 x+2)^5}-33275 \log (3 x+2)+33275 \log (5 x+3) \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {343}{9 (2+3 x)^6}-\frac {1421}{9 (2+3 x)^5}-\frac {7189}{9 (2+3 x)^4}-\frac {3993}{(2+3 x)^3}-\frac {19965}{(2+3 x)^2}-\frac {99825}{2+3 x}+\frac {166375}{3+5 x}\right ) \, dx \\ & = \frac {343}{135 (2+3 x)^5}+\frac {1421}{108 (2+3 x)^4}+\frac {7189}{81 (2+3 x)^3}+\frac {1331}{2 (2+3 x)^2}+\frac {6655}{2+3 x}-33275 \log (2+3 x)+33275 \log (3+5 x) \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 50, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x)^3}{(2+3 x)^6 (3+5 x)} \, dx=\frac {181744346+1075586865 x+2388229560 x^2+2357826570 x^3+873269100 x^4}{1620 (2+3 x)^5}-33275 \log (5 (2+3 x))+33275 \log (3+5 x) \]
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Time = 2.44 (sec) , antiderivative size = 46, normalized size of antiderivative = 0.66
method | result | size |
norman | \(\frac {539055 x^{4}+\frac {2910897}{2} x^{3}+\frac {13267942}{9} x^{2}+\frac {71705791}{108} x +\frac {90872173}{810}}{\left (2+3 x \right )^{5}}-33275 \ln \left (2+3 x \right )+33275 \ln \left (3+5 x \right )\) | \(46\) |
risch | \(\frac {539055 x^{4}+\frac {2910897}{2} x^{3}+\frac {13267942}{9} x^{2}+\frac {71705791}{108} x +\frac {90872173}{810}}{\left (2+3 x \right )^{5}}-33275 \ln \left (2+3 x \right )+33275 \ln \left (3+5 x \right )\) | \(47\) |
default | \(\frac {343}{135 \left (2+3 x \right )^{5}}+\frac {1421}{108 \left (2+3 x \right )^{4}}+\frac {7189}{81 \left (2+3 x \right )^{3}}+\frac {1331}{2 \left (2+3 x \right )^{2}}+\frac {6655}{2+3 x}-33275 \ln \left (2+3 x \right )+33275 \ln \left (3+5 x \right )\) | \(63\) |
parallelrisch | \(-\frac {7762392000 \ln \left (\frac {2}{3}+x \right ) x^{5}-7762392000 \ln \left (x +\frac {3}{5}\right ) x^{5}+25874640000 \ln \left (\frac {2}{3}+x \right ) x^{4}-25874640000 \ln \left (x +\frac {3}{5}\right ) x^{4}+817849557 x^{5}+34499520000 \ln \left (\frac {2}{3}+x \right ) x^{3}-34499520000 \ln \left (x +\frac {3}{5}\right ) x^{3}+2208672390 x^{4}+22999680000 \ln \left (\frac {2}{3}+x \right ) x^{2}-22999680000 \ln \left (x +\frac {3}{5}\right ) x^{2}+2237656360 x^{3}+7666560000 \ln \left (\frac {2}{3}+x \right ) x -7666560000 \ln \left (x +\frac {3}{5}\right ) x +1008010800 x^{2}+1022208000 \ln \left (\frac {2}{3}+x \right )-1022208000 \ln \left (x +\frac {3}{5}\right )+170367840 x}{960 \left (2+3 x \right )^{5}}\) | \(132\) |
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Time = 0.23 (sec) , antiderivative size = 115, normalized size of antiderivative = 1.64 \[ \int \frac {(1-2 x)^3}{(2+3 x)^6 (3+5 x)} \, dx=\frac {873269100 \, x^{4} + 2357826570 \, x^{3} + 2388229560 \, x^{2} + 53905500 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (5 \, x + 3\right ) - 53905500 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (3 \, x + 2\right ) + 1075586865 \, x + 181744346}{1620 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
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Time = 0.09 (sec) , antiderivative size = 63, normalized size of antiderivative = 0.90 \[ \int \frac {(1-2 x)^3}{(2+3 x)^6 (3+5 x)} \, dx=- \frac {- 873269100 x^{4} - 2357826570 x^{3} - 2388229560 x^{2} - 1075586865 x - 181744346}{393660 x^{5} + 1312200 x^{4} + 1749600 x^{3} + 1166400 x^{2} + 388800 x + 51840} + 33275 \log {\left (x + \frac {3}{5} \right )} - 33275 \log {\left (x + \frac {2}{3} \right )} \]
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Time = 0.27 (sec) , antiderivative size = 66, normalized size of antiderivative = 0.94 \[ \int \frac {(1-2 x)^3}{(2+3 x)^6 (3+5 x)} \, dx=\frac {873269100 \, x^{4} + 2357826570 \, x^{3} + 2388229560 \, x^{2} + 1075586865 \, x + 181744346}{1620 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} + 33275 \, \log \left (5 \, x + 3\right ) - 33275 \, \log \left (3 \, x + 2\right ) \]
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Time = 0.27 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.69 \[ \int \frac {(1-2 x)^3}{(2+3 x)^6 (3+5 x)} \, dx=\frac {873269100 \, x^{4} + 2357826570 \, x^{3} + 2388229560 \, x^{2} + 1075586865 \, x + 181744346}{1620 \, {\left (3 \, x + 2\right )}^{5}} + 33275 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 33275 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
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Time = 0.05 (sec) , antiderivative size = 55, normalized size of antiderivative = 0.79 \[ \int \frac {(1-2 x)^3}{(2+3 x)^6 (3+5 x)} \, dx=\frac {\frac {6655\,x^4}{3}+\frac {11979\,x^3}{2}+\frac {13267942\,x^2}{2187}+\frac {71705791\,x}{26244}+\frac {90872173}{196830}}{x^5+\frac {10\,x^4}{3}+\frac {40\,x^3}{9}+\frac {80\,x^2}{27}+\frac {80\,x}{81}+\frac {32}{243}}-66550\,\mathrm {atanh}\left (30\,x+19\right ) \]
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