Integrand size = 22, antiderivative size = 101 \[ \int \frac {(1-2 x)^2}{(2+3 x)^7 (3+5 x)^3} \, dx=\frac {49}{6 (2+3 x)^6}+\frac {707}{5 (2+3 x)^5}+\frac {3467}{2 (2+3 x)^4}+\frac {57110}{3 (2+3 x)^3}+\frac {424975}{2 (2+3 x)^2}+\frac {2958125}{2+3 x}-\frac {75625}{2 (3+5 x)^2}+\frac {1615625}{3+5 x}-19637500 \log (2+3 x)+19637500 \log (3+5 x) \]
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Time = 0.04 (sec) , antiderivative size = 101, 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} \[ \int \frac {(1-2 x)^2}{(2+3 x)^7 (3+5 x)^3} \, dx=\frac {2958125}{3 x+2}+\frac {1615625}{5 x+3}+\frac {424975}{2 (3 x+2)^2}-\frac {75625}{2 (5 x+3)^2}+\frac {57110}{3 (3 x+2)^3}+\frac {3467}{2 (3 x+2)^4}+\frac {707}{5 (3 x+2)^5}+\frac {49}{6 (3 x+2)^6}-19637500 \log (3 x+2)+19637500 \log (5 x+3) \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {147}{(2+3 x)^7}-\frac {2121}{(2+3 x)^6}-\frac {20802}{(2+3 x)^5}-\frac {171330}{(2+3 x)^4}-\frac {1274925}{(2+3 x)^3}-\frac {8874375}{(2+3 x)^2}-\frac {58912500}{2+3 x}+\frac {378125}{(3+5 x)^3}-\frac {8078125}{(3+5 x)^2}+\frac {98187500}{3+5 x}\right ) \, dx \\ & = \frac {49}{6 (2+3 x)^6}+\frac {707}{5 (2+3 x)^5}+\frac {3467}{2 (2+3 x)^4}+\frac {57110}{3 (2+3 x)^3}+\frac {424975}{2 (2+3 x)^2}+\frac {2958125}{2+3 x}-\frac {75625}{2 (3+5 x)^2}+\frac {1615625}{3+5 x}-19637500 \log (2+3 x)+19637500 \log (3+5 x) \\ \end{align*}
Time = 0.05 (sec) , antiderivative size = 103, normalized size of antiderivative = 1.02 \[ \int \frac {(1-2 x)^2}{(2+3 x)^7 (3+5 x)^3} \, dx=\frac {49}{6 (2+3 x)^6}+\frac {707}{5 (2+3 x)^5}+\frac {3467}{2 (2+3 x)^4}+\frac {57110}{3 (2+3 x)^3}+\frac {424975}{2 (2+3 x)^2}+\frac {2958125}{2+3 x}-\frac {75625}{2 (3+5 x)^2}+\frac {1615625}{3+5 x}-19637500 \log (5 (2+3 x))+19637500 \log (3+5 x) \]
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Time = 2.34 (sec) , antiderivative size = 68, normalized size of antiderivative = 0.67
method | result | size |
norman | \(\frac {23859562500 x^{7}+59018836277 x^{2}+108958668750 x^{6}+150974686710 x^{3}+213180772500 x^{5}+231644539125 x^{4}+\frac {64065488324}{5} x +\frac {11917538647}{10}}{\left (2+3 x \right )^{6} \left (3+5 x \right )^{2}}-19637500 \ln \left (2+3 x \right )+19637500 \ln \left (3+5 x \right )\) | \(68\) |
risch | \(\frac {23859562500 x^{7}+59018836277 x^{2}+108958668750 x^{6}+150974686710 x^{3}+213180772500 x^{5}+231644539125 x^{4}+\frac {64065488324}{5} x +\frac {11917538647}{10}}{\left (2+3 x \right )^{6} \left (3+5 x \right )^{2}}-19637500 \ln \left (2+3 x \right )+19637500 \ln \left (3+5 x \right )\) | \(69\) |
default | \(\frac {49}{6 \left (2+3 x \right )^{6}}+\frac {707}{5 \left (2+3 x \right )^{5}}+\frac {3467}{2 \left (2+3 x \right )^{4}}+\frac {57110}{3 \left (2+3 x \right )^{3}}+\frac {424975}{2 \left (2+3 x \right )^{2}}+\frac {2958125}{2+3 x}-\frac {75625}{2 \left (3+5 x \right )^{2}}+\frac {1615625}{3+5 x}-19637500 \ln \left (2+3 x \right )+19637500 \ln \left (3+5 x \right )\) | \(90\) |
parallelrisch | \(-\frac {10858751999040 x -4334451840000000 \ln \left (x +\frac {3}{5}\right ) x^{2}+13356264960000000 \ln \left (\frac {2}{3}+x \right ) x^{3}-803547648000000 \ln \left (x +\frac {3}{5}\right ) x +4334451840000000 \ln \left (\frac {2}{3}+x \right ) x^{2}+803547648000000 \ln \left (\frac {2}{3}+x \right ) x +2109513943260468 x^{5}+1941116265513027 x^{6}+991994057576190 x^{7}+537608767988160 x^{3}+1375060690648980 x^{4}+116731583997520 x^{2}+217197141841575 x^{8}+25714882080000000 \ln \left (\frac {2}{3}+x \right ) x^{4}+65152512000000 \ln \left (\frac {2}{3}+x \right )+10719624240000000 \ln \left (\frac {2}{3}+x \right ) x^{7}-10719624240000000 \ln \left (x +\frac {3}{5}\right ) x^{7}-65152512000000 \ln \left (x +\frac {3}{5}\right )+31676336928000000 \ln \left (\frac {2}{3}+x \right ) x^{5}-13356264960000000 \ln \left (x +\frac {3}{5}\right ) x^{3}-31676336928000000 \ln \left (x +\frac {3}{5}\right ) x^{5}-25714882080000000 \ln \left (x +\frac {3}{5}\right ) x^{4}+24380273592000000 \ln \left (\frac {2}{3}+x \right ) x^{6}-24380273592000000 \ln \left (x +\frac {3}{5}\right ) x^{6}+2061466200000000 \ln \left (\frac {2}{3}+x \right ) x^{8}-2061466200000000 \ln \left (x +\frac {3}{5}\right ) x^{8}}{5760 \left (2+3 x \right )^{6} \left (3+5 x \right )^{2}}\) | \(208\) |
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Time = 0.22 (sec) , antiderivative size = 175, normalized size of antiderivative = 1.73 \[ \int \frac {(1-2 x)^2}{(2+3 x)^7 (3+5 x)^3} \, dx=\frac {238595625000 \, x^{7} + 1089586687500 \, x^{6} + 2131807725000 \, x^{5} + 2316445391250 \, x^{4} + 1509746867100 \, x^{3} + 590188362770 \, x^{2} + 196375000 \, {\left (18225 \, x^{8} + 94770 \, x^{7} + 215541 \, x^{6} + 280044 \, x^{5} + 227340 \, x^{4} + 118080 \, x^{3} + 38320 \, x^{2} + 7104 \, x + 576\right )} \log \left (5 \, x + 3\right ) - 196375000 \, {\left (18225 \, x^{8} + 94770 \, x^{7} + 215541 \, x^{6} + 280044 \, x^{5} + 227340 \, x^{4} + 118080 \, x^{3} + 38320 \, x^{2} + 7104 \, x + 576\right )} \log \left (3 \, x + 2\right ) + 128130976648 \, x + 11917538647}{10 \, {\left (18225 \, x^{8} + 94770 \, x^{7} + 215541 \, x^{6} + 280044 \, x^{5} + 227340 \, x^{4} + 118080 \, x^{3} + 38320 \, x^{2} + 7104 \, x + 576\right )}} \]
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Time = 0.10 (sec) , antiderivative size = 92, normalized size of antiderivative = 0.91 \[ \int \frac {(1-2 x)^2}{(2+3 x)^7 (3+5 x)^3} \, dx=\frac {238595625000 x^{7} + 1089586687500 x^{6} + 2131807725000 x^{5} + 2316445391250 x^{4} + 1509746867100 x^{3} + 590188362770 x^{2} + 128130976648 x + 11917538647}{182250 x^{8} + 947700 x^{7} + 2155410 x^{6} + 2800440 x^{5} + 2273400 x^{4} + 1180800 x^{3} + 383200 x^{2} + 71040 x + 5760} + 19637500 \log {\left (x + \frac {3}{5} \right )} - 19637500 \log {\left (x + \frac {2}{3} \right )} \]
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Time = 0.22 (sec) , antiderivative size = 96, normalized size of antiderivative = 0.95 \[ \int \frac {(1-2 x)^2}{(2+3 x)^7 (3+5 x)^3} \, dx=\frac {238595625000 \, x^{7} + 1089586687500 \, x^{6} + 2131807725000 \, x^{5} + 2316445391250 \, x^{4} + 1509746867100 \, x^{3} + 590188362770 \, x^{2} + 128130976648 \, x + 11917538647}{10 \, {\left (18225 \, x^{8} + 94770 \, x^{7} + 215541 \, x^{6} + 280044 \, x^{5} + 227340 \, x^{4} + 118080 \, x^{3} + 38320 \, x^{2} + 7104 \, x + 576\right )}} + 19637500 \, \log \left (5 \, x + 3\right ) - 19637500 \, \log \left (3 \, x + 2\right ) \]
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Time = 0.28 (sec) , antiderivative size = 70, normalized size of antiderivative = 0.69 \[ \int \frac {(1-2 x)^2}{(2+3 x)^7 (3+5 x)^3} \, dx=\frac {238595625000 \, x^{7} + 1089586687500 \, x^{6} + 2131807725000 \, x^{5} + 2316445391250 \, x^{4} + 1509746867100 \, x^{3} + 590188362770 \, x^{2} + 128130976648 \, x + 11917538647}{10 \, {\left (5 \, x + 3\right )}^{2} {\left (3 \, x + 2\right )}^{6}} + 19637500 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 19637500 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
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Time = 1.44 (sec) , antiderivative size = 85, normalized size of antiderivative = 0.84 \[ \int \frac {(1-2 x)^2}{(2+3 x)^7 (3+5 x)^3} \, dx=\frac {\frac {3927500\,x^7}{3}+\frac {53806750\,x^6}{9}+\frac {947470100\,x^5}{81}+\frac {114392365\,x^4}{9}+\frac {3354993038\,x^3}{405}+\frac {59018836277\,x^2}{18225}+\frac {64065488324\,x}{91125}+\frac {11917538647}{182250}}{x^8+\frac {26\,x^7}{5}+\frac {887\,x^6}{75}+\frac {10372\,x^5}{675}+\frac {1684\,x^4}{135}+\frac {2624\,x^3}{405}+\frac {7664\,x^2}{3645}+\frac {2368\,x}{6075}+\frac {64}{2025}}-39275000\,\mathrm {atanh}\left (30\,x+19\right ) \]
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