Integrand size = 22, antiderivative size = 77 \[ \int \frac {(1-2 x)^2}{(2+3 x)^5 (3+5 x)^3} \, dx=\frac {49}{4 (2+3 x)^4}+\frac {707}{3 (2+3 x)^3}+\frac {3467}{(2+3 x)^2}+\frac {57110}{2+3 x}-\frac {3025}{2 (3+5 x)^2}+\frac {46475}{3+5 x}-424975 \log (2+3 x)+424975 \log (3+5 x) \]
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Time = 0.03 (sec) , antiderivative size = 77, 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} \[ \int \frac {(1-2 x)^2}{(2+3 x)^5 (3+5 x)^3} \, dx=\frac {57110}{3 x+2}+\frac {46475}{5 x+3}+\frac {3467}{(3 x+2)^2}-\frac {3025}{2 (5 x+3)^2}+\frac {707}{3 (3 x+2)^3}+\frac {49}{4 (3 x+2)^4}-424975 \log (3 x+2)+424975 \log (5 x+3) \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {147}{(2+3 x)^5}-\frac {2121}{(2+3 x)^4}-\frac {20802}{(2+3 x)^3}-\frac {171330}{(2+3 x)^2}-\frac {1274925}{2+3 x}+\frac {15125}{(3+5 x)^3}-\frac {232375}{(3+5 x)^2}+\frac {2124875}{3+5 x}\right ) \, dx \\ & = \frac {49}{4 (2+3 x)^4}+\frac {707}{3 (2+3 x)^3}+\frac {3467}{(2+3 x)^2}+\frac {57110}{2+3 x}-\frac {3025}{2 (3+5 x)^2}+\frac {46475}{3+5 x}-424975 \log (2+3 x)+424975 \log (3+5 x) \\ \end{align*}
Time = 0.04 (sec) , antiderivative size = 79, normalized size of antiderivative = 1.03 \[ \int \frac {(1-2 x)^2}{(2+3 x)^5 (3+5 x)^3} \, dx=\frac {49}{4 (2+3 x)^4}+\frac {707}{3 (2+3 x)^3}+\frac {3467}{(2+3 x)^2}+\frac {57110}{2+3 x}-\frac {3025}{2 (3+5 x)^2}+\frac {46475}{3+5 x}-424975 \log (5 (2+3 x))+424975 \log (3+5 x) \]
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Time = 2.37 (sec) , antiderivative size = 58, normalized size of antiderivative = 0.75
method | result | size |
norman | \(\frac {57371625 x^{5}+239770895 x^{3}+\frac {99957973}{2} x +\frac {371003175}{2} x^{4}+\frac {1858347679}{12} x^{2}+\frac {25790737}{4}}{\left (2+3 x \right )^{4} \left (3+5 x \right )^{2}}-424975 \ln \left (2+3 x \right )+424975 \ln \left (3+5 x \right )\) | \(58\) |
risch | \(\frac {57371625 x^{5}+239770895 x^{3}+\frac {99957973}{2} x +\frac {371003175}{2} x^{4}+\frac {1858347679}{12} x^{2}+\frac {25790737}{4}}{\left (2+3 x \right )^{4} \left (3+5 x \right )^{2}}-424975 \ln \left (2+3 x \right )+424975 \ln \left (3+5 x \right )\) | \(59\) |
default | \(\frac {49}{4 \left (2+3 x \right )^{4}}+\frac {707}{3 \left (2+3 x \right )^{3}}+\frac {3467}{\left (2+3 x \right )^{2}}+\frac {57110}{2+3 x}-\frac {3025}{2 \left (3+5 x \right )^{2}}+\frac {46475}{3+5 x}-424975 \ln \left (2+3 x \right )+424975 \ln \left (3+5 x \right )\) | \(72\) |
parallelrisch | \(-\frac {5874854304 x -1278759974400 \ln \left (x +\frac {3}{5}\right ) x^{2}+2649559334400 \ln \left (\frac {2}{3}+x \right ) x^{3}-328991846400 \ln \left (x +\frac {3}{5}\right ) x +1278759974400 \ln \left (\frac {2}{3}+x \right ) x^{2}+328991846400 \ln \left (\frac {2}{3}+x \right ) x +168895414710 x^{5}+52226242425 x^{6}+141050901768 x^{3}+218346488433 x^{4}+45530121496 x^{2}+3086501630400 \ln \left (\frac {2}{3}+x \right ) x^{4}+35249126400 \ln \left (\frac {2}{3}+x \right )-35249126400 \ln \left (x +\frac {3}{5}\right )+1916671248000 \ln \left (\frac {2}{3}+x \right ) x^{5}-2649559334400 \ln \left (x +\frac {3}{5}\right ) x^{3}-1916671248000 \ln \left (x +\frac {3}{5}\right ) x^{5}-3086501630400 \ln \left (x +\frac {3}{5}\right ) x^{4}+495690840000 \ln \left (\frac {2}{3}+x \right ) x^{6}-495690840000 \ln \left (x +\frac {3}{5}\right ) x^{6}}{576 \left (2+3 x \right )^{4} \left (3+5 x \right )^{2}}\) | \(162\) |
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Time = 0.22 (sec) , antiderivative size = 135, normalized size of antiderivative = 1.75 \[ \int \frac {(1-2 x)^2}{(2+3 x)^5 (3+5 x)^3} \, dx=\frac {688459500 \, x^{5} + 2226019050 \, x^{4} + 2877250740 \, x^{3} + 1858347679 \, x^{2} + 5099700 \, {\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )} \log \left (5 \, x + 3\right ) - 5099700 \, {\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )} \log \left (3 \, x + 2\right ) + 599747838 \, x + 77372211}{12 \, {\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )}} \]
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Time = 0.09 (sec) , antiderivative size = 71, normalized size of antiderivative = 0.92 \[ \int \frac {(1-2 x)^2}{(2+3 x)^5 (3+5 x)^3} \, dx=\frac {688459500 x^{5} + 2226019050 x^{4} + 2877250740 x^{3} + 1858347679 x^{2} + 599747838 x + 77372211}{24300 x^{6} + 93960 x^{5} + 151308 x^{4} + 129888 x^{3} + 62688 x^{2} + 16128 x + 1728} + 424975 \log {\left (x + \frac {3}{5} \right )} - 424975 \log {\left (x + \frac {2}{3} \right )} \]
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Time = 0.21 (sec) , antiderivative size = 76, normalized size of antiderivative = 0.99 \[ \int \frac {(1-2 x)^2}{(2+3 x)^5 (3+5 x)^3} \, dx=\frac {688459500 \, x^{5} + 2226019050 \, x^{4} + 2877250740 \, x^{3} + 1858347679 \, x^{2} + 599747838 \, x + 77372211}{12 \, {\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )}} + 424975 \, \log \left (5 \, x + 3\right ) - 424975 \, \log \left (3 \, x + 2\right ) \]
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Time = 0.28 (sec) , antiderivative size = 76, normalized size of antiderivative = 0.99 \[ \int \frac {(1-2 x)^2}{(2+3 x)^5 (3+5 x)^3} \, dx=\frac {57110}{3 \, x + 2} - \frac {4125 \, {\left (\frac {404}{3 \, x + 2} - 1855\right )}}{2 \, {\left (\frac {1}{3 \, x + 2} - 5\right )}^{2}} + \frac {3467}{{\left (3 \, x + 2\right )}^{2}} + \frac {707}{3 \, {\left (3 \, x + 2\right )}^{3}} + \frac {49}{4 \, {\left (3 \, x + 2\right )}^{4}} + 424975 \, \log \left ({\left | -\frac {1}{3 \, x + 2} + 5 \right |}\right ) \]
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Time = 1.49 (sec) , antiderivative size = 65, normalized size of antiderivative = 0.84 \[ \int \frac {(1-2 x)^2}{(2+3 x)^5 (3+5 x)^3} \, dx=\frac {\frac {84995\,x^5}{3}+\frac {1648903\,x^4}{18}+\frac {47954179\,x^3}{405}+\frac {1858347679\,x^2}{24300}+\frac {99957973\,x}{4050}+\frac {25790737}{8100}}{x^6+\frac {58\,x^5}{15}+\frac {467\,x^4}{75}+\frac {3608\,x^3}{675}+\frac {5224\,x^2}{2025}+\frac {448\,x}{675}+\frac {16}{225}}-849950\,\mathrm {atanh}\left (30\,x+19\right ) \]
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