Integrand size = 22, antiderivative size = 77 \[ \int \frac {(1-2 x)^2}{(2+3 x)^6 (3+5 x)^2} \, dx=-\frac {49}{15 (2+3 x)^5}-\frac {77}{2 (2+3 x)^4}-\frac {1133}{3 (2+3 x)^3}-\frac {3740}{(2+3 x)^2}-\frac {46475}{2+3 x}-\frac {15125}{3+5 x}+277750 \log (2+3 x)-277750 \log (3+5 x) \]
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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} \[ \int \frac {(1-2 x)^2}{(2+3 x)^6 (3+5 x)^2} \, dx=-\frac {46475}{3 x+2}-\frac {15125}{5 x+3}-\frac {3740}{(3 x+2)^2}-\frac {1133}{3 (3 x+2)^3}-\frac {77}{2 (3 x+2)^4}-\frac {49}{15 (3 x+2)^5}+277750 \log (3 x+2)-277750 \log (5 x+3) \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {49}{(2+3 x)^6}+\frac {462}{(2+3 x)^5}+\frac {3399}{(2+3 x)^4}+\frac {22440}{(2+3 x)^3}+\frac {139425}{(2+3 x)^2}+\frac {833250}{2+3 x}+\frac {75625}{(3+5 x)^2}-\frac {1388750}{3+5 x}\right ) \, dx \\ & = -\frac {49}{15 (2+3 x)^5}-\frac {77}{2 (2+3 x)^4}-\frac {1133}{3 (2+3 x)^3}-\frac {3740}{(2+3 x)^2}-\frac {46475}{2+3 x}-\frac {15125}{3+5 x}+277750 \log (2+3 x)-277750 \log (3+5 x) \\ \end{align*}
Time = 0.05 (sec) , antiderivative size = 62, normalized size of antiderivative = 0.81 \[ \int \frac {(1-2 x)^2}{(2+3 x)^6 (3+5 x)^2} \, dx=-\frac {84279984+639246515 x+1938789435 x^2+2939206050 x^3+2227277250 x^4+674932500 x^5}{30 (2+3 x)^5 (3+5 x)}+277750 \log (5 (2+3 x))-277750 \log (3+5 x) \]
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Time = 2.35 (sec) , antiderivative size = 58, normalized size of antiderivative = 0.75
method | result | size |
norman | \(\frac {-97973535 x^{3}-74242575 x^{4}-22497750 x^{5}-\frac {129252629}{2} x^{2}-\frac {127849303}{6} x -\frac {14046664}{5}}{\left (2+3 x \right )^{5} \left (3+5 x \right )}+277750 \ln \left (2+3 x \right )-277750 \ln \left (3+5 x \right )\) | \(58\) |
risch | \(\frac {-97973535 x^{3}-74242575 x^{4}-22497750 x^{5}-\frac {129252629}{2} x^{2}-\frac {127849303}{6} x -\frac {14046664}{5}}{\left (2+3 x \right )^{5} \left (3+5 x \right )}+277750 \ln \left (2+3 x \right )-277750 \ln \left (3+5 x \right )\) | \(59\) |
default | \(-\frac {49}{15 \left (2+3 x \right )^{5}}-\frac {77}{2 \left (2+3 x \right )^{4}}-\frac {1133}{3 \left (2+3 x \right )^{3}}-\frac {3740}{\left (2+3 x \right )^{2}}-\frac {46475}{2+3 x}-\frac {15125}{3+5 x}+277750 \ln \left (2+3 x \right )-277750 \ln \left (3+5 x \right )\) | \(72\) |
parallelrisch | \(\frac {2133120080 x -447955200000 \ln \left (x +\frac {3}{5}\right ) x^{2}+911908800000 \ln \left (\frac {2}{3}+x \right ) x^{3}-117321600000 \ln \left (x +\frac {3}{5}\right ) x +447955200000 \ln \left (\frac {2}{3}+x \right ) x^{2}+117321600000 \ln \left (\frac {2}{3}+x \right ) x +56330087256 x^{5}+17066696760 x^{6}+49051884960 x^{3}+74348943120 x^{4}+16176160080 x^{2}+1043895600000 \ln \left (\frac {2}{3}+x \right ) x^{4}+12798720000 \ln \left (\frac {2}{3}+x \right )-12798720000 \ln \left (x +\frac {3}{5}\right )+637136280000 \ln \left (\frac {2}{3}+x \right ) x^{5}-911908800000 \ln \left (x +\frac {3}{5}\right ) x^{3}-637136280000 \ln \left (x +\frac {3}{5}\right ) x^{5}-1043895600000 \ln \left (x +\frac {3}{5}\right ) x^{4}+161983800000 \ln \left (\frac {2}{3}+x \right ) x^{6}-161983800000 \ln \left (x +\frac {3}{5}\right ) x^{6}}{480 \left (2+3 x \right )^{5} \left (3+5 x \right )}\) | \(162\) |
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Time = 0.23 (sec) , antiderivative size = 135, normalized size of antiderivative = 1.75 \[ \int \frac {(1-2 x)^2}{(2+3 x)^6 (3+5 x)^2} \, dx=-\frac {674932500 \, x^{5} + 2227277250 \, x^{4} + 2939206050 \, x^{3} + 1938789435 \, x^{2} + 8332500 \, {\left (1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right )} \log \left (5 \, x + 3\right ) - 8332500 \, {\left (1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right )} \log \left (3 \, x + 2\right ) + 639246515 \, x + 84279984}{30 \, {\left (1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right )}} \]
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Time = 0.09 (sec) , antiderivative size = 73, normalized size of antiderivative = 0.95 \[ \int \frac {(1-2 x)^2}{(2+3 x)^6 (3+5 x)^2} \, dx=\frac {- 674932500 x^{5} - 2227277250 x^{4} - 2939206050 x^{3} - 1938789435 x^{2} - 639246515 x - 84279984}{36450 x^{6} + 143370 x^{5} + 234900 x^{4} + 205200 x^{3} + 100800 x^{2} + 26400 x + 2880} - 277750 \log {\left (x + \frac {3}{5} \right )} + 277750 \log {\left (x + \frac {2}{3} \right )} \]
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Time = 0.20 (sec) , antiderivative size = 76, normalized size of antiderivative = 0.99 \[ \int \frac {(1-2 x)^2}{(2+3 x)^6 (3+5 x)^2} \, dx=-\frac {674932500 \, x^{5} + 2227277250 \, x^{4} + 2939206050 \, x^{3} + 1938789435 \, x^{2} + 639246515 \, x + 84279984}{30 \, {\left (1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right )}} - 277750 \, \log \left (5 \, x + 3\right ) + 277750 \, \log \left (3 \, x + 2\right ) \]
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Time = 0.28 (sec) , antiderivative size = 76, normalized size of antiderivative = 0.99 \[ \int \frac {(1-2 x)^2}{(2+3 x)^6 (3+5 x)^2} \, dx=-\frac {15125}{5 \, x + 3} + \frac {125 \, {\left (\frac {2338497}{5 \, x + 3} + \frac {1317834}{{\left (5 \, x + 3\right )}^{2}} + \frac {338628}{{\left (5 \, x + 3\right )}^{3}} + \frac {33998}{{\left (5 \, x + 3\right )}^{4}} + 1583793\right )}}{2 \, {\left (\frac {1}{5 \, x + 3} + 3\right )}^{5}} + 277750 \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) \]
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Time = 1.34 (sec) , antiderivative size = 66, normalized size of antiderivative = 0.86 \[ \int \frac {(1-2 x)^2}{(2+3 x)^6 (3+5 x)^2} \, dx=555500\,\mathrm {atanh}\left (30\,x+19\right )-\frac {\frac {55550\,x^5}{3}+61105\,x^4+\frac {6531569\,x^3}{81}+\frac {129252629\,x^2}{2430}+\frac {127849303\,x}{7290}+\frac {14046664}{6075}}{x^6+\frac {59\,x^5}{15}+\frac {58\,x^4}{9}+\frac {152\,x^3}{27}+\frac {224\,x^2}{81}+\frac {176\,x}{243}+\frac {32}{405}} \]
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