Integrand size = 22, antiderivative size = 73 \[ \int \frac {(1-2 x)^2 (2+3 x)^6}{(3+5 x)^3} \, dx=\frac {920502 x}{390625}+\frac {189 x^2}{15625}-\frac {16299 x^3}{3125}-\frac {23571 x^4}{12500}+\frac {17496 x^5}{3125}+\frac {486 x^6}{125}-\frac {121}{3906250 (3+5 x)^2}-\frac {2134}{1953125 (3+5 x)}+\frac {15547 \log (3+5 x)}{1953125} \]
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Time = 0.03 (sec) , antiderivative size = 73, 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} \[ \int \frac {(1-2 x)^2 (2+3 x)^6}{(3+5 x)^3} \, dx=\frac {486 x^6}{125}+\frac {17496 x^5}{3125}-\frac {23571 x^4}{12500}-\frac {16299 x^3}{3125}+\frac {189 x^2}{15625}+\frac {920502 x}{390625}-\frac {2134}{1953125 (5 x+3)}-\frac {121}{3906250 (5 x+3)^2}+\frac {15547 \log (5 x+3)}{1953125} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {920502}{390625}+\frac {378 x}{15625}-\frac {48897 x^2}{3125}-\frac {23571 x^3}{3125}+\frac {17496 x^4}{625}+\frac {2916 x^5}{125}+\frac {121}{390625 (3+5 x)^3}+\frac {2134}{390625 (3+5 x)^2}+\frac {15547}{390625 (3+5 x)}\right ) \, dx \\ & = \frac {920502 x}{390625}+\frac {189 x^2}{15625}-\frac {16299 x^3}{3125}-\frac {23571 x^4}{12500}+\frac {17496 x^5}{3125}+\frac {486 x^6}{125}-\frac {121}{3906250 (3+5 x)^2}-\frac {2134}{1953125 (3+5 x)}+\frac {15547 \log (3+5 x)}{1953125} \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 68, normalized size of antiderivative = 0.93 \[ \int \frac {(1-2 x)^2 (2+3 x)^6}{(3+5 x)^3} \, dx=\frac {274543613+1743814610 x+3528738675 x^2+481792500 x^3-6763246875 x^4-5334918750 x^5+6086390625 x^6+10023750000 x^7+3796875000 x^8+310940 (3+5 x)^2 \log (6 (3+5 x))}{39062500 (3+5 x)^2} \]
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Time = 0.78 (sec) , antiderivative size = 52, normalized size of antiderivative = 0.71
method | result | size |
risch | \(\frac {486 x^{6}}{125}+\frac {17496 x^{5}}{3125}-\frac {23571 x^{4}}{12500}-\frac {16299 x^{3}}{3125}+\frac {189 x^{2}}{15625}+\frac {920502 x}{390625}+\frac {-\frac {2134 x}{390625}-\frac {517}{156250}}{\left (3+5 x \right )^{2}}+\frac {15547 \ln \left (3+5 x \right )}{1953125}\) | \(52\) |
default | \(\frac {920502 x}{390625}+\frac {189 x^{2}}{15625}-\frac {16299 x^{3}}{3125}-\frac {23571 x^{4}}{12500}+\frac {17496 x^{5}}{3125}+\frac {486 x^{6}}{125}-\frac {121}{3906250 \left (3+5 x \right )^{2}}-\frac {2134}{1953125 \left (3+5 x \right )}+\frac {15547 \ln \left (3+5 x \right )}{1953125}\) | \(56\) |
norman | \(\frac {\frac {24860077}{1171875} x +\frac {99580231}{1406250} x^{2}+\frac {192717}{15625} x^{3}-\frac {2164239}{12500} x^{4}-\frac {853587}{6250} x^{5}+\frac {389529}{2500} x^{6}+\frac {32076}{125} x^{7}+\frac {486}{5} x^{8}}{\left (3+5 x \right )^{2}}+\frac {15547 \ln \left (3+5 x \right )}{1953125}\) | \(57\) |
parallelrisch | \(\frac {6834375000 x^{8}+18042750000 x^{7}+10955503125 x^{6}-9602853750 x^{5}-12173844375 x^{4}+13992300 \ln \left (x +\frac {3}{5}\right ) x^{2}+867226500 x^{3}+16790760 \ln \left (x +\frac {3}{5}\right ) x +4979011550 x^{2}+5037228 \ln \left (x +\frac {3}{5}\right )+1491604620 x}{70312500 \left (3+5 x \right )^{2}}\) | \(71\) |
meijerg | \(\frac {32 x \left (\frac {5 x}{3}+2\right )}{27 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {160 x^{2}}{27 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {56 x \left (15 x +6\right )}{225 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {15547 \ln \left (1+\frac {5 x}{3}\right )}{1953125}-\frac {504 x \left (\frac {100}{9} x^{2}+30 x +12\right )}{125 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {1134 x \left (-\frac {625}{27} x^{3}+\frac {500}{9} x^{2}+150 x +60\right )}{625 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {1134 x \left (\frac {1250}{81} x^{4}-\frac {625}{27} x^{3}+\frac {500}{9} x^{2}+150 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {6561 x \left (-\frac {21875}{243} x^{5}+\frac {8750}{81} x^{4}-\frac {4375}{27} x^{3}+\frac {3500}{9} x^{2}+1050 x +420\right )}{12500 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {177147 x \left (\frac {125000}{729} x^{6}-\frac {43750}{243} x^{5}+\frac {17500}{81} x^{4}-\frac {8750}{27} x^{3}+\frac {7000}{9} x^{2}+2100 x +840\right )}{781250 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {39366 x \left (-\frac {390625}{729} x^{7}+\frac {125000}{243} x^{6}-\frac {43750}{81} x^{5}+\frac {17500}{27} x^{4}-\frac {8750}{9} x^{3}+\frac {7000}{3} x^{2}+6300 x +2520\right )}{1953125 \left (1+\frac {5 x}{3}\right )^{2}}\) | \(247\) |
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Time = 0.23 (sec) , antiderivative size = 72, normalized size of antiderivative = 0.99 \[ \int \frac {(1-2 x)^2 (2+3 x)^6}{(3+5 x)^3} \, dx=\frac {759375000 \, x^{8} + 2004750000 \, x^{7} + 1217278125 \, x^{6} - 1066983750 \, x^{5} - 1352649375 \, x^{4} + 96358500 \, x^{3} + 553151700 \, x^{2} + 62188 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 165647680 \, x - 25850}{7812500 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
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Time = 0.06 (sec) , antiderivative size = 65, normalized size of antiderivative = 0.89 \[ \int \frac {(1-2 x)^2 (2+3 x)^6}{(3+5 x)^3} \, dx=\frac {486 x^{6}}{125} + \frac {17496 x^{5}}{3125} - \frac {23571 x^{4}}{12500} - \frac {16299 x^{3}}{3125} + \frac {189 x^{2}}{15625} + \frac {920502 x}{390625} + \frac {- 4268 x - 2585}{19531250 x^{2} + 23437500 x + 7031250} + \frac {15547 \log {\left (5 x + 3 \right )}}{1953125} \]
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Time = 0.20 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.77 \[ \int \frac {(1-2 x)^2 (2+3 x)^6}{(3+5 x)^3} \, dx=\frac {486}{125} \, x^{6} + \frac {17496}{3125} \, x^{5} - \frac {23571}{12500} \, x^{4} - \frac {16299}{3125} \, x^{3} + \frac {189}{15625} \, x^{2} + \frac {920502}{390625} \, x - \frac {11 \, {\left (388 \, x + 235\right )}}{781250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {15547}{1953125} \, \log \left (5 \, x + 3\right ) \]
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Time = 0.28 (sec) , antiderivative size = 52, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x)^2 (2+3 x)^6}{(3+5 x)^3} \, dx=\frac {486}{125} \, x^{6} + \frac {17496}{3125} \, x^{5} - \frac {23571}{12500} \, x^{4} - \frac {16299}{3125} \, x^{3} + \frac {189}{15625} \, x^{2} + \frac {920502}{390625} \, x - \frac {11 \, {\left (388 \, x + 235\right )}}{781250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {15547}{1953125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
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Time = 0.04 (sec) , antiderivative size = 52, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x)^2 (2+3 x)^6}{(3+5 x)^3} \, dx=\frac {920502\,x}{390625}+\frac {15547\,\ln \left (x+\frac {3}{5}\right )}{1953125}-\frac {\frac {2134\,x}{9765625}+\frac {517}{3906250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}}+\frac {189\,x^2}{15625}-\frac {16299\,x^3}{3125}-\frac {23571\,x^4}{12500}+\frac {17496\,x^5}{3125}+\frac {486\,x^6}{125} \]
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