Integrand size = 20, antiderivative size = 66 \[ \int \frac {(1-2 x) (2+3 x)^6}{(3+5 x)^3} \, dx=\frac {36936 x}{15625}+\frac {297 x^2}{125}-\frac {6399 x^3}{3125}-\frac {12393 x^4}{2500}-\frac {1458 x^5}{625}-\frac {11}{781250 (3+5 x)^2}-\frac {196}{390625 (3+5 x)}+\frac {1449 \log (3+5 x)}{390625} \]
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Time = 0.02 (sec) , antiderivative size = 66, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78} \[ \int \frac {(1-2 x) (2+3 x)^6}{(3+5 x)^3} \, dx=-\frac {1458 x^5}{625}-\frac {12393 x^4}{2500}-\frac {6399 x^3}{3125}+\frac {297 x^2}{125}+\frac {36936 x}{15625}-\frac {196}{390625 (5 x+3)}-\frac {11}{781250 (5 x+3)^2}+\frac {1449 \log (5 x+3)}{390625} \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {36936}{15625}+\frac {594 x}{125}-\frac {19197 x^2}{3125}-\frac {12393 x^3}{625}-\frac {1458 x^4}{125}+\frac {11}{78125 (3+5 x)^3}+\frac {196}{78125 (3+5 x)^2}+\frac {1449}{78125 (3+5 x)}\right ) \, dx \\ & = \frac {36936 x}{15625}+\frac {297 x^2}{125}-\frac {6399 x^3}{3125}-\frac {12393 x^4}{2500}-\frac {1458 x^5}{625}-\frac {11}{781250 (3+5 x)^2}-\frac {196}{390625 (3+5 x)}+\frac {1449 \log (3+5 x)}{390625} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 61, normalized size of antiderivative = 0.92 \[ \int \frac {(1-2 x) (2+3 x)^6}{(3+5 x)^3} \, dx=\frac {40891591+302537270 x+834723225 x^2+874597500 x^3-364415625 x^4-1725806250 x^5-1514953125 x^6-455625000 x^7+28980 (3+5 x)^2 \log (3+5 x)}{7812500 (3+5 x)^2} \]
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Time = 0.72 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.71
method | result | size |
risch | \(-\frac {1458 x^{5}}{625}-\frac {12393 x^{4}}{2500}-\frac {6399 x^{3}}{3125}+\frac {297 x^{2}}{125}+\frac {36936 x}{15625}+\frac {-\frac {196 x}{78125}-\frac {1187}{781250}}{\left (3+5 x \right )^{2}}+\frac {1449 \ln \left (3+5 x \right )}{390625}\) | \(47\) |
default | \(\frac {36936 x}{15625}+\frac {297 x^{2}}{125}-\frac {6399 x^{3}}{3125}-\frac {12393 x^{4}}{2500}-\frac {1458 x^{5}}{625}-\frac {11}{781250 \left (3+5 x \right )^{2}}-\frac {196}{390625 \left (3+5 x \right )}+\frac {1449 \ln \left (3+5 x \right )}{390625}\) | \(51\) |
norman | \(\frac {\frac {4986959}{234375} x +\frac {25960877}{281250} x^{2}+\frac {349839}{3125} x^{3}-\frac {116613}{2500} x^{4}-\frac {276129}{1250} x^{5}-\frac {96957}{500} x^{6}-\frac {1458}{25} x^{7}}{\left (3+5 x \right )^{2}}+\frac {1449 \ln \left (3+5 x \right )}{390625}\) | \(52\) |
parallelrisch | \(\frac {-820125000 x^{7}-2726915625 x^{6}-3106451250 x^{5}-655948125 x^{4}+1304100 \ln \left (x +\frac {3}{5}\right ) x^{2}+1574275500 x^{3}+1564920 \ln \left (x +\frac {3}{5}\right ) x +1298043850 x^{2}+469476 \ln \left (x +\frac {3}{5}\right )+299217540 x}{14062500 \left (3+5 x \right )^{2}}\) | \(66\) |
meijerg | \(\frac {32 x \left (\frac {5 x}{3}+2\right )}{27 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {224 x^{2}}{27 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {56 x \left (15 x +6\right )}{25 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {1449 \ln \left (1+\frac {5 x}{3}\right )}{390625}+\frac {1134 x \left (-\frac {625}{27} x^{3}+\frac {500}{9} x^{2}+150 x +60\right )}{625 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {10206 x \left (\frac {1250}{81} x^{4}-\frac {625}{27} x^{3}+\frac {500}{9} x^{2}+150 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {19683 x \left (-\frac {21875}{243} x^{5}+\frac {8750}{81} x^{4}-\frac {4375}{27} x^{3}+\frac {3500}{9} x^{2}+1050 x +420\right )}{62500 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {59049 x \left (\frac {125000}{729} x^{6}-\frac {43750}{243} x^{5}+\frac {17500}{81} x^{4}-\frac {8750}{27} x^{3}+\frac {7000}{9} x^{2}+2100 x +840\right )}{1562500 \left (1+\frac {5 x}{3}\right )^{2}}\) | \(182\) |
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Time = 0.25 (sec) , antiderivative size = 67, normalized size of antiderivative = 1.02 \[ \int \frac {(1-2 x) (2+3 x)^6}{(3+5 x)^3} \, dx=-\frac {91125000 \, x^{7} + 302990625 \, x^{6} + 345161250 \, x^{5} + 72883125 \, x^{4} - 174919500 \, x^{3} - 144220500 \, x^{2} - 5796 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 33238480 \, x + 2374}{1562500 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
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Time = 0.06 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.85 \[ \int \frac {(1-2 x) (2+3 x)^6}{(3+5 x)^3} \, dx=- \frac {1458 x^{5}}{625} - \frac {12393 x^{4}}{2500} - \frac {6399 x^{3}}{3125} + \frac {297 x^{2}}{125} + \frac {36936 x}{15625} - \frac {1960 x + 1187}{19531250 x^{2} + 23437500 x + 7031250} + \frac {1449 \log {\left (5 x + 3 \right )}}{390625} \]
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Time = 0.23 (sec) , antiderivative size = 51, normalized size of antiderivative = 0.77 \[ \int \frac {(1-2 x) (2+3 x)^6}{(3+5 x)^3} \, dx=-\frac {1458}{625} \, x^{5} - \frac {12393}{2500} \, x^{4} - \frac {6399}{3125} \, x^{3} + \frac {297}{125} \, x^{2} + \frac {36936}{15625} \, x - \frac {1960 \, x + 1187}{781250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {1449}{390625} \, \log \left (5 \, x + 3\right ) \]
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Time = 0.28 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x) (2+3 x)^6}{(3+5 x)^3} \, dx=-\frac {1458}{625} \, x^{5} - \frac {12393}{2500} \, x^{4} - \frac {6399}{3125} \, x^{3} + \frac {297}{125} \, x^{2} + \frac {36936}{15625} \, x - \frac {1960 \, x + 1187}{781250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {1449}{390625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
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Time = 0.05 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x) (2+3 x)^6}{(3+5 x)^3} \, dx=\frac {36936\,x}{15625}+\frac {1449\,\ln \left (x+\frac {3}{5}\right )}{390625}-\frac {\frac {196\,x}{1953125}+\frac {1187}{19531250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}}+\frac {297\,x^2}{125}-\frac {6399\,x^3}{3125}-\frac {12393\,x^4}{2500}-\frac {1458\,x^5}{625} \]
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