Integrand size = 22, antiderivative size = 62 \[ \int \frac {(1-2 x)^2 (2+3 x)^5}{(3+5 x)^2} \, dx=\frac {277174 x}{78125}+\frac {1893 x^2}{6250}-\frac {25332 x^3}{3125}-\frac {8721 x^4}{2500}+\frac {5508 x^5}{625}+\frac {162 x^6}{25}-\frac {121}{390625 (3+5 x)}+\frac {1771 \log (3+5 x)}{390625} \]
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Time = 0.02 (sec) , antiderivative size = 62, 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} \[ \int \frac {(1-2 x)^2 (2+3 x)^5}{(3+5 x)^2} \, dx=\frac {162 x^6}{25}+\frac {5508 x^5}{625}-\frac {8721 x^4}{2500}-\frac {25332 x^3}{3125}+\frac {1893 x^2}{6250}+\frac {277174 x}{78125}-\frac {121}{390625 (5 x+3)}+\frac {1771 \log (5 x+3)}{390625} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {277174}{78125}+\frac {1893 x}{3125}-\frac {75996 x^2}{3125}-\frac {8721 x^3}{625}+\frac {5508 x^4}{125}+\frac {972 x^5}{25}+\frac {121}{78125 (3+5 x)^2}+\frac {1771}{78125 (3+5 x)}\right ) \, dx \\ & = \frac {277174 x}{78125}+\frac {1893 x^2}{6250}-\frac {25332 x^3}{3125}-\frac {8721 x^4}{2500}+\frac {5508 x^5}{625}+\frac {162 x^6}{25}-\frac {121}{390625 (3+5 x)}+\frac {1771 \log (3+5 x)}{390625} \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 61, normalized size of antiderivative = 0.98 \[ \int \frac {(1-2 x)^2 (2+3 x)^5}{(3+5 x)^2} \, dx=\frac {25866973+126267855 x+145685750 x^2-178158750 x^3-398409375 x^4+70284375 x^5+496125000 x^6+253125000 x^7+35420 (3+5 x) \log (6 (3+5 x))}{7812500 (3+5 x)} \]
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Time = 0.78 (sec) , antiderivative size = 45, normalized size of antiderivative = 0.73
method | result | size |
risch | \(\frac {162 x^{6}}{25}+\frac {5508 x^{5}}{625}-\frac {8721 x^{4}}{2500}-\frac {25332 x^{3}}{3125}+\frac {1893 x^{2}}{6250}+\frac {277174 x}{78125}-\frac {121}{1953125 \left (x +\frac {3}{5}\right )}+\frac {1771 \ln \left (3+5 x \right )}{390625}\) | \(45\) |
default | \(\frac {277174 x}{78125}+\frac {1893 x^{2}}{6250}-\frac {25332 x^{3}}{3125}-\frac {8721 x^{4}}{2500}+\frac {5508 x^{5}}{625}+\frac {162 x^{6}}{25}-\frac {121}{390625 \left (3+5 x \right )}+\frac {1771 \ln \left (3+5 x \right )}{390625}\) | \(47\) |
norman | \(\frac {\frac {2494687}{234375} x +\frac {582743}{31250} x^{2}-\frac {142527}{6250} x^{3}-\frac {127491}{2500} x^{4}+\frac {22491}{2500} x^{5}+\frac {7938}{125} x^{6}+\frac {162}{5} x^{7}}{3+5 x}+\frac {1771 \ln \left (3+5 x \right )}{390625}\) | \(52\) |
parallelrisch | \(\frac {151875000 x^{7}+297675000 x^{6}+42170625 x^{5}-239045625 x^{4}-106895250 x^{3}+106260 \ln \left (x +\frac {3}{5}\right ) x +87411450 x^{2}+63756 \ln \left (x +\frac {3}{5}\right )+49893740 x}{14062500+23437500 x}\) | \(57\) |
meijerg | \(-\frac {176 x}{45 \left (1+\frac {5 x}{3}\right )}+\frac {1771 \ln \left (1+\frac {5 x}{3}\right )}{390625}-\frac {112 x \left (5 x +6\right )}{75 \left (1+\frac {5 x}{3}\right )}+\frac {126 x \left (-\frac {50}{9} x^{2}+10 x +12\right )}{25 \left (1+\frac {5 x}{3}\right )}-\frac {378 x \left (\frac {625}{27} x^{3}-\frac {250}{9} x^{2}+50 x +60\right )}{625 \left (1+\frac {5 x}{3}\right )}-\frac {11907 x \left (-\frac {625}{27} x^{4}+\frac {625}{27} x^{3}-\frac {250}{9} x^{2}+50 x +60\right )}{12500 \left (1+\frac {5 x}{3}\right )}+\frac {13122 x \left (\frac {43750}{243} x^{5}-\frac {4375}{27} x^{4}+\frac {4375}{27} x^{3}-\frac {1750}{9} x^{2}+350 x +420\right )}{78125 \left (1+\frac {5 x}{3}\right )}-\frac {19683 x \left (-\frac {312500}{729} x^{6}+\frac {87500}{243} x^{5}-\frac {8750}{27} x^{4}+\frac {8750}{27} x^{3}-\frac {3500}{9} x^{2}+700 x +840\right )}{781250 \left (1+\frac {5 x}{3}\right )}\) | \(185\) |
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Time = 0.22 (sec) , antiderivative size = 57, normalized size of antiderivative = 0.92 \[ \int \frac {(1-2 x)^2 (2+3 x)^5}{(3+5 x)^2} \, dx=\frac {50625000 \, x^{7} + 99225000 \, x^{6} + 14056875 \, x^{5} - 79681875 \, x^{4} - 35631750 \, x^{3} + 29137150 \, x^{2} + 7084 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 16630440 \, x - 484}{1562500 \, {\left (5 \, x + 3\right )}} \]
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Time = 0.05 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.87 \[ \int \frac {(1-2 x)^2 (2+3 x)^5}{(3+5 x)^2} \, dx=\frac {162 x^{6}}{25} + \frac {5508 x^{5}}{625} - \frac {8721 x^{4}}{2500} - \frac {25332 x^{3}}{3125} + \frac {1893 x^{2}}{6250} + \frac {277174 x}{78125} + \frac {1771 \log {\left (5 x + 3 \right )}}{390625} - \frac {121}{1953125 x + 1171875} \]
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Time = 0.19 (sec) , antiderivative size = 46, normalized size of antiderivative = 0.74 \[ \int \frac {(1-2 x)^2 (2+3 x)^5}{(3+5 x)^2} \, dx=\frac {162}{25} \, x^{6} + \frac {5508}{625} \, x^{5} - \frac {8721}{2500} \, x^{4} - \frac {25332}{3125} \, x^{3} + \frac {1893}{6250} \, x^{2} + \frac {277174}{78125} \, x - \frac {121}{390625 \, {\left (5 \, x + 3\right )}} + \frac {1771}{390625} \, \log \left (5 \, x + 3\right ) \]
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Time = 0.29 (sec) , antiderivative size = 84, normalized size of antiderivative = 1.35 \[ \int \frac {(1-2 x)^2 (2+3 x)^5}{(3+5 x)^2} \, dx=-\frac {1}{7812500} \, {\left (5 \, x + 3\right )}^{6} {\left (\frac {36288}{5 \, x + 3} - \frac {63315}{{\left (5 \, x + 3\right )}^{2}} - \frac {249900}{{\left (5 \, x + 3\right )}^{3}} - \frac {287700}{{\left (5 \, x + 3\right )}^{4}} - \frac {204680}{{\left (5 \, x + 3\right )}^{5}} - 3240\right )} - \frac {121}{390625 \, {\left (5 \, x + 3\right )}} - \frac {1771}{390625} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) \]
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Time = 0.06 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x)^2 (2+3 x)^5}{(3+5 x)^2} \, dx=\frac {277174\,x}{78125}+\frac {1771\,\ln \left (x+\frac {3}{5}\right )}{390625}-\frac {121}{1953125\,\left (x+\frac {3}{5}\right )}+\frac {1893\,x^2}{6250}-\frac {25332\,x^3}{3125}-\frac {8721\,x^4}{2500}+\frac {5508\,x^5}{625}+\frac {162\,x^6}{25} \]
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