Integrand size = 22, antiderivative size = 57 \[ \int \frac {(1-2 x)^3}{(2+3 x)^3 (3+5 x)^3} \, dx=\frac {343}{6 (2+3 x)^2}+\frac {1617}{2+3 x}-\frac {1331}{10 (3+5 x)^2}+\frac {2541}{3+5 x}-15708 \log (2+3 x)+15708 \log (3+5 x) \]
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Time = 0.02 (sec) , antiderivative size = 57, 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} \[ \int \frac {(1-2 x)^3}{(2+3 x)^3 (3+5 x)^3} \, dx=\frac {1617}{3 x+2}+\frac {2541}{5 x+3}+\frac {343}{6 (3 x+2)^2}-\frac {1331}{10 (5 x+3)^2}-15708 \log (3 x+2)+15708 \log (5 x+3) \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {343}{(2+3 x)^3}-\frac {4851}{(2+3 x)^2}-\frac {47124}{2+3 x}+\frac {1331}{(3+5 x)^3}-\frac {12705}{(3+5 x)^2}+\frac {78540}{3+5 x}\right ) \, dx \\ & = \frac {343}{6 (2+3 x)^2}+\frac {1617}{2+3 x}-\frac {1331}{10 (3+5 x)^2}+\frac {2541}{3+5 x}-15708 \log (2+3 x)+15708 \log (3+5 x) \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.04 \[ \int \frac {(1-2 x)^3}{(2+3 x)^3 (3+5 x)^3} \, dx=\frac {343}{6 (2+3 x)^2}+\frac {1617}{2+3 x}-\frac {1331}{10 (3+5 x)^2}+\frac {2541}{3+5 x}-15708 \log (5 (2+3 x))+15708 \log (3+5 x) \]
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Time = 2.43 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.84
method | result | size |
norman | \(\frac {235620 x^{3}+\frac {1415464}{5} x +\frac {6715174}{15} x^{2}+\frac {595801}{10}}{\left (2+3 x \right )^{2} \left (3+5 x \right )^{2}}-15708 \ln \left (2+3 x \right )+15708 \ln \left (3+5 x \right )\) | \(48\) |
risch | \(\frac {235620 x^{3}+\frac {1415464}{5} x +\frac {6715174}{15} x^{2}+\frac {595801}{10}}{\left (2+3 x \right )^{2} \left (3+5 x \right )^{2}}-15708 \ln \left (2+3 x \right )+15708 \ln \left (3+5 x \right )\) | \(49\) |
default | \(\frac {343}{6 \left (2+3 x \right )^{2}}+\frac {1617}{2+3 x}-\frac {1331}{10 \left (3+5 x \right )^{2}}+\frac {2541}{3+5 x}-15708 \ln \left (2+3 x \right )+15708 \ln \left (3+5 x \right )\) | \(54\) |
parallelrisch | \(-\frac {254469600 \ln \left (\frac {2}{3}+x \right ) x^{4}-254469600 \ln \left (x +\frac {3}{5}\right ) x^{4}+644656320 \ln \left (\frac {2}{3}+x \right ) x^{3}-644656320 \ln \left (x +\frac {3}{5}\right ) x^{3}+26811045 x^{4}+611858016 \ln \left (\frac {2}{3}+x \right ) x^{2}-611858016 \ln \left (x +\frac {3}{5}\right ) x^{2}+50956674 x^{3}+257862528 \ln \left (\frac {2}{3}+x \right ) x -257862528 \ln \left (x +\frac {3}{5}\right ) x +32232833 x^{2}+40715136 \ln \left (\frac {2}{3}+x \right )-40715136 \ln \left (x +\frac {3}{5}\right )+6785844 x}{72 \left (2+3 x \right )^{2} \left (3+5 x \right )^{2}}\) | \(116\) |
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Time = 0.22 (sec) , antiderivative size = 95, normalized size of antiderivative = 1.67 \[ \int \frac {(1-2 x)^3}{(2+3 x)^3 (3+5 x)^3} \, dx=\frac {7068600 \, x^{3} + 13430348 \, x^{2} + 471240 \, {\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )} \log \left (5 \, x + 3\right ) - 471240 \, {\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )} \log \left (3 \, x + 2\right ) + 8492784 \, x + 1787403}{30 \, {\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )}} \]
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Time = 0.07 (sec) , antiderivative size = 53, normalized size of antiderivative = 0.93 \[ \int \frac {(1-2 x)^3}{(2+3 x)^3 (3+5 x)^3} \, dx=- \frac {- 7068600 x^{3} - 13430348 x^{2} - 8492784 x - 1787403}{6750 x^{4} + 17100 x^{3} + 16230 x^{2} + 6840 x + 1080} + 15708 \log {\left (x + \frac {3}{5} \right )} - 15708 \log {\left (x + \frac {2}{3} \right )} \]
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Time = 0.21 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.98 \[ \int \frac {(1-2 x)^3}{(2+3 x)^3 (3+5 x)^3} \, dx=\frac {7068600 \, x^{3} + 13430348 \, x^{2} + 8492784 \, x + 1787403}{30 \, {\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )}} + 15708 \, \log \left (5 \, x + 3\right ) - 15708 \, \log \left (3 \, x + 2\right ) \]
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Time = 0.42 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.84 \[ \int \frac {(1-2 x)^3}{(2+3 x)^3 (3+5 x)^3} \, dx=\frac {7068600 \, x^{3} + 13430348 \, x^{2} + 8492784 \, x + 1787403}{30 \, {\left (15 \, x^{2} + 19 \, x + 6\right )}^{2}} + 15708 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 15708 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
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Time = 1.25 (sec) , antiderivative size = 45, normalized size of antiderivative = 0.79 \[ \int \frac {(1-2 x)^3}{(2+3 x)^3 (3+5 x)^3} \, dx=\frac {\frac {5236\,x^3}{5}+\frac {6715174\,x^2}{3375}+\frac {1415464\,x}{1125}+\frac {595801}{2250}}{x^4+\frac {38\,x^3}{15}+\frac {541\,x^2}{225}+\frac {76\,x}{75}+\frac {4}{25}}-31416\,\mathrm {atanh}\left (30\,x+19\right ) \]
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