Integrand size = 22, antiderivative size = 68 \[ \int \frac {(1-2 x)^3}{(2+3 x)^5 (3+5 x)^2} \, dx=-\frac {343}{36 (2+3 x)^4}-\frac {3136}{27 (2+3 x)^3}-\frac {2541}{2 (2+3 x)^2}-\frac {16698}{2+3 x}-\frac {6655}{3+5 x}+103455 \log (2+3 x)-103455 \log (3+5 x) \]
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Time = 0.02 (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} \[ \int \frac {(1-2 x)^3}{(2+3 x)^5 (3+5 x)^2} \, dx=-\frac {16698}{3 x+2}-\frac {6655}{5 x+3}-\frac {2541}{2 (3 x+2)^2}-\frac {3136}{27 (3 x+2)^3}-\frac {343}{36 (3 x+2)^4}+103455 \log (3 x+2)-103455 \log (5 x+3) \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {343}{3 (2+3 x)^5}+\frac {3136}{3 (2+3 x)^4}+\frac {7623}{(2+3 x)^3}+\frac {50094}{(2+3 x)^2}+\frac {310365}{2+3 x}+\frac {33275}{(3+5 x)^2}-\frac {517275}{3+5 x}\right ) \, dx \\ & = -\frac {343}{36 (2+3 x)^4}-\frac {3136}{27 (2+3 x)^3}-\frac {2541}{2 (2+3 x)^2}-\frac {16698}{2+3 x}-\frac {6655}{3+5 x}+103455 \log (2+3 x)-103455 \log (3+5 x) \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 70, normalized size of antiderivative = 1.03 \[ \int \frac {(1-2 x)^3}{(2+3 x)^5 (3+5 x)^2} \, dx=-\frac {343}{36 (2+3 x)^4}-\frac {3136}{27 (2+3 x)^3}-\frac {2541}{2 (2+3 x)^2}-\frac {16698}{2+3 x}-\frac {6655}{3+5 x}+103455 \log (5 (2+3 x))-103455 \log (3+5 x) \]
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Time = 2.46 (sec) , antiderivative size = 53, normalized size of antiderivative = 0.78
method | result | size |
norman | \(\frac {-2793285 x^{4}-\frac {343827337}{108} x -\frac {130688491}{18} x^{2}-\frac {14711301}{2} x^{3}-\frac {18835325}{36}}{\left (2+3 x \right )^{4} \left (3+5 x \right )}+103455 \ln \left (2+3 x \right )-103455 \ln \left (3+5 x \right )\) | \(53\) |
risch | \(\frac {-2793285 x^{4}-\frac {343827337}{108} x -\frac {130688491}{18} x^{2}-\frac {14711301}{2} x^{3}-\frac {18835325}{36}}{\left (2+3 x \right )^{4} \left (3+5 x \right )}+103455 \ln \left (2+3 x \right )-103455 \ln \left (3+5 x \right )\) | \(54\) |
default | \(-\frac {343}{36 \left (2+3 x \right )^{4}}-\frac {3136}{27 \left (2+3 x \right )^{3}}-\frac {2541}{2 \left (2+3 x \right )^{2}}-\frac {16698}{2+3 x}-\frac {6655}{3+5 x}+103455 \ln \left (2+3 x \right )-103455 \ln \left (3+5 x \right )\) | \(63\) |
parallelrisch | \(\frac {8044660800 \ln \left (\frac {2}{3}+x \right ) x^{5}-8044660800 \ln \left (x +\frac {3}{5}\right ) x^{5}+26279225280 \ln \left (\frac {2}{3}+x \right ) x^{4}-26279225280 \ln \left (x +\frac {3}{5}\right ) x^{4}+847589625 x^{5}+34323886080 \ln \left (\frac {2}{3}+x \right ) x^{3}-34323886080 \ln \left (x +\frac {3}{5}\right ) x^{3}+2232482055 x^{4}+22405870080 \ln \left (\frac {2}{3}+x \right ) x^{2}-22405870080 \ln \left (x +\frac {3}{5}\right ) x^{2}+2204097504 x^{3}+7309716480 \ln \left (\frac {2}{3}+x \right ) x -7309716480 \ln \left (x +\frac {3}{5}\right ) x +966683496 x^{2}+953441280 \ln \left (\frac {2}{3}+x \right )-953441280 \ln \left (x +\frac {3}{5}\right )+158906912 x}{192 \left (2+3 x \right )^{4} \left (3+5 x \right )}\) | \(139\) |
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Time = 0.22 (sec) , antiderivative size = 115, normalized size of antiderivative = 1.69 \[ \int \frac {(1-2 x)^3}{(2+3 x)^5 (3+5 x)^2} \, dx=-\frac {301674780 \, x^{4} + 794410254 \, x^{3} + 784130946 \, x^{2} + 11173140 \, {\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )} \log \left (5 \, x + 3\right ) - 11173140 \, {\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )} \log \left (3 \, x + 2\right ) + 343827337 \, x + 56505975}{108 \, {\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )}} \]
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Time = 0.08 (sec) , antiderivative size = 61, normalized size of antiderivative = 0.90 \[ \int \frac {(1-2 x)^3}{(2+3 x)^5 (3+5 x)^2} \, dx=- \frac {301674780 x^{4} + 794410254 x^{3} + 784130946 x^{2} + 343827337 x + 56505975}{43740 x^{5} + 142884 x^{4} + 186624 x^{3} + 121824 x^{2} + 39744 x + 5184} - 103455 \log {\left (x + \frac {3}{5} \right )} + 103455 \log {\left (x + \frac {2}{3} \right )} \]
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Time = 0.21 (sec) , antiderivative size = 66, normalized size of antiderivative = 0.97 \[ \int \frac {(1-2 x)^3}{(2+3 x)^5 (3+5 x)^2} \, dx=-\frac {301674780 \, x^{4} + 794410254 \, x^{3} + 784130946 \, x^{2} + 343827337 \, x + 56505975}{108 \, {\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )}} - 103455 \, \log \left (5 \, x + 3\right ) + 103455 \, \log \left (3 \, x + 2\right ) \]
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Time = 0.31 (sec) , antiderivative size = 67, normalized size of antiderivative = 0.99 \[ \int \frac {(1-2 x)^3}{(2+3 x)^5 (3+5 x)^2} \, dx=-\frac {6655}{5 \, x + 3} + \frac {5 \, {\left (\frac {9923332}{5 \, x + 3} + \frac {3831284}{{\left (5 \, x + 3\right )}^{2}} + \frac {514536}{{\left (5 \, x + 3\right )}^{3}} + 8795037\right )}}{4 \, {\left (\frac {1}{5 \, x + 3} + 3\right )}^{4}} + 103455 \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) \]
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Time = 1.26 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.82 \[ \int \frac {(1-2 x)^3}{(2+3 x)^5 (3+5 x)^2} \, dx=206910\,\mathrm {atanh}\left (30\,x+19\right )-\frac {6897\,x^4+\frac {181621\,x^3}{10}+\frac {130688491\,x^2}{7290}+\frac {343827337\,x}{43740}+\frac {3767065}{2916}}{x^5+\frac {49\,x^4}{15}+\frac {64\,x^3}{15}+\frac {376\,x^2}{135}+\frac {368\,x}{405}+\frac {16}{135}} \]
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