Integrand size = 22, antiderivative size = 68 \[ \int \frac {(1-2 x)^3}{(2+3 x)^4 (3+5 x)^3} \, dx=\frac {343}{9 (2+3 x)^3}+\frac {1617}{2 (2+3 x)^2}+\frac {15708}{2+3 x}-\frac {1331}{2 (3+5 x)^2}+\frac {16698}{3+5 x}-128634 \log (2+3 x)+128634 \log (3+5 x) \]
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Time = 0.03 (sec) , antiderivative size = 68, 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} \[ \int \frac {(1-2 x)^3}{(2+3 x)^4 (3+5 x)^3} \, dx=\frac {15708}{3 x+2}+\frac {16698}{5 x+3}+\frac {1617}{2 (3 x+2)^2}-\frac {1331}{2 (5 x+3)^2}+\frac {343}{9 (3 x+2)^3}-128634 \log (3 x+2)+128634 \log (5 x+3) \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {343}{(2+3 x)^4}-\frac {4851}{(2+3 x)^3}-\frac {47124}{(2+3 x)^2}-\frac {385902}{2+3 x}+\frac {6655}{(3+5 x)^3}-\frac {83490}{(3+5 x)^2}+\frac {643170}{3+5 x}\right ) \, dx \\ & = \frac {343}{9 (2+3 x)^3}+\frac {1617}{2 (2+3 x)^2}+\frac {15708}{2+3 x}-\frac {1331}{2 (3+5 x)^2}+\frac {16698}{3+5 x}-128634 \log (2+3 x)+128634 \log (3+5 x) \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 70, normalized size of antiderivative = 1.03 \[ \int \frac {(1-2 x)^3}{(2+3 x)^4 (3+5 x)^3} \, dx=\frac {343}{9 (2+3 x)^3}+\frac {1617}{2 (2+3 x)^2}+\frac {15708}{2+3 x}-\frac {1331}{2 (3+5 x)^2}+\frac {16698}{3+5 x}-128634 \log (5 (2+3 x))+128634 \log (3+5 x) \]
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Time = 2.48 (sec) , antiderivative size = 53, normalized size of antiderivative = 0.78
method | result | size |
norman | \(\frac {5788530 x^{4}+14857227 x^{3}+\frac {36601517}{6} x +\frac {128582548}{9} x^{2}+975812}{\left (2+3 x \right )^{3} \left (3+5 x \right )^{2}}-128634 \ln \left (2+3 x \right )+128634 \ln \left (3+5 x \right )\) | \(53\) |
risch | \(\frac {5788530 x^{4}+14857227 x^{3}+\frac {36601517}{6} x +\frac {128582548}{9} x^{2}+975812}{\left (2+3 x \right )^{3} \left (3+5 x \right )^{2}}-128634 \ln \left (2+3 x \right )+128634 \ln \left (3+5 x \right )\) | \(54\) |
default | \(\frac {343}{9 \left (2+3 x \right )^{3}}+\frac {1617}{2 \left (2+3 x \right )^{2}}+\frac {15708}{2+3 x}-\frac {1331}{2 \left (3+5 x \right )^{2}}+\frac {16698}{3+5 x}-128634 \ln \left (2+3 x \right )+128634 \ln \left (3+5 x \right )\) | \(63\) |
parallelrisch | \(-\frac {6251612400 \ln \left (\frac {2}{3}+x \right ) x^{5}-6251612400 \ln \left (x +\frac {3}{5}\right ) x^{5}+20005159680 \ln \left (\frac {2}{3}+x \right ) x^{4}-20005159680 \ln \left (x +\frac {3}{5}\right ) x^{4}+658673100 x^{5}+25589933424 \ln \left (\frac {2}{3}+x \right ) x^{3}-25589933424 \ln \left (x +\frac {3}{5}\right ) x^{3}+1690979760 x^{4}+16356070368 \ln \left (\frac {2}{3}+x \right ) x^{2}-16356070368 \ln \left (x +\frac {3}{5}\right ) x^{2}+1626448212 x^{3}+5223569472 \ln \left (\frac {2}{3}+x \right ) x -5223569472 \ln \left (x +\frac {3}{5}\right ) x +694623608 x^{2}+666838656 \ln \left (\frac {2}{3}+x \right )-666838656 \ln \left (x +\frac {3}{5}\right )+111139764 x}{72 \left (2+3 x \right )^{3} \left (3+5 x \right )^{2}}\) | \(139\) |
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Time = 0.21 (sec) , antiderivative size = 115, normalized size of antiderivative = 1.69 \[ \int \frac {(1-2 x)^3}{(2+3 x)^4 (3+5 x)^3} \, dx=\frac {104193540 \, x^{4} + 267430086 \, x^{3} + 257165096 \, x^{2} + 2315412 \, {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )} \log \left (5 \, x + 3\right ) - 2315412 \, {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )} \log \left (3 \, x + 2\right ) + 109804551 \, x + 17564616}{18 \, {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )}} \]
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Time = 0.09 (sec) , antiderivative size = 63, normalized size of antiderivative = 0.93 \[ \int \frac {(1-2 x)^3}{(2+3 x)^4 (3+5 x)^3} \, dx=- \frac {- 104193540 x^{4} - 267430086 x^{3} - 257165096 x^{2} - 109804551 x - 17564616}{12150 x^{5} + 38880 x^{4} + 49734 x^{3} + 31788 x^{2} + 10152 x + 1296} + 128634 \log {\left (x + \frac {3}{5} \right )} - 128634 \log {\left (x + \frac {2}{3} \right )} \]
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Time = 0.25 (sec) , antiderivative size = 66, normalized size of antiderivative = 0.97 \[ \int \frac {(1-2 x)^3}{(2+3 x)^4 (3+5 x)^3} \, dx=\frac {104193540 \, x^{4} + 267430086 \, x^{3} + 257165096 \, x^{2} + 109804551 \, x + 17564616}{18 \, {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )}} + 128634 \, \log \left (5 \, x + 3\right ) - 128634 \, \log \left (3 \, x + 2\right ) \]
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Time = 0.42 (sec) , antiderivative size = 55, normalized size of antiderivative = 0.81 \[ \int \frac {(1-2 x)^3}{(2+3 x)^4 (3+5 x)^3} \, dx=\frac {104193540 \, x^{4} + 267430086 \, x^{3} + 257165096 \, x^{2} + 109804551 \, x + 17564616}{18 \, {\left (5 \, x + 3\right )}^{2} {\left (3 \, x + 2\right )}^{3}} + 128634 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 128634 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
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Time = 1.22 (sec) , antiderivative size = 55, normalized size of antiderivative = 0.81 \[ \int \frac {(1-2 x)^3}{(2+3 x)^4 (3+5 x)^3} \, dx=\frac {\frac {42878\,x^4}{5}+\frac {1650803\,x^3}{75}+\frac {128582548\,x^2}{6075}+\frac {36601517\,x}{4050}+\frac {975812}{675}}{x^5+\frac {16\,x^4}{5}+\frac {307\,x^3}{75}+\frac {1766\,x^2}{675}+\frac {188\,x}{225}+\frac {8}{75}}-257268\,\mathrm {atanh}\left (30\,x+19\right ) \]
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