Integrand size = 22, antiderivative size = 77 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^7} \, dx=\frac {343}{13122 (2+3 x)^6}-\frac {1813}{3645 (2+3 x)^5}+\frac {10073}{2916 (2+3 x)^4}-\frac {66193}{6561 (2+3 x)^3}+\frac {7195}{729 (2+3 x)^2}-\frac {3700}{729 (2+3 x)}-\frac {1000 \log (2+3 x)}{2187} \]
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Time = 0.02 (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} \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^7} \, dx=-\frac {3700}{729 (3 x+2)}+\frac {7195}{729 (3 x+2)^2}-\frac {66193}{6561 (3 x+2)^3}+\frac {10073}{2916 (3 x+2)^4}-\frac {1813}{3645 (3 x+2)^5}+\frac {343}{13122 (3 x+2)^6}-\frac {1000 \log (3 x+2)}{2187} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {343}{729 (2+3 x)^7}+\frac {1813}{243 (2+3 x)^6}-\frac {10073}{243 (2+3 x)^5}+\frac {66193}{729 (2+3 x)^4}-\frac {14390}{243 (2+3 x)^3}+\frac {3700}{243 (2+3 x)^2}-\frac {1000}{729 (2+3 x)}\right ) \, dx \\ & = \frac {343}{13122 (2+3 x)^6}-\frac {1813}{3645 (2+3 x)^5}+\frac {10073}{2916 (2+3 x)^4}-\frac {66193}{6561 (2+3 x)^3}+\frac {7195}{729 (2+3 x)^2}-\frac {3700}{729 (2+3 x)}-\frac {1000 \log (2+3 x)}{2187} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 51, normalized size of antiderivative = 0.66 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^7} \, dx=-\frac {3165082+25975248 x+89062425 x^2+158427540 x^3+144852300 x^4+53946000 x^5+20000 (2+3 x)^6 \log (2+3 x)}{43740 (2+3 x)^6} \]
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Time = 2.44 (sec) , antiderivative size = 43, normalized size of antiderivative = 0.56
method | result | size |
norman | \(\frac {-\frac {2164604}{3645} x -\frac {1979165}{972} x^{2}-\frac {880153}{243} x^{3}-\frac {9935}{3} x^{4}-\frac {3700}{3} x^{5}-\frac {1582541}{21870}}{\left (2+3 x \right )^{6}}-\frac {1000 \ln \left (2+3 x \right )}{2187}\) | \(43\) |
risch | \(\frac {-\frac {2164604}{3645} x -\frac {1979165}{972} x^{2}-\frac {880153}{243} x^{3}-\frac {9935}{3} x^{4}-\frac {3700}{3} x^{5}-\frac {1582541}{21870}}{\left (2+3 x \right )^{6}}-\frac {1000 \ln \left (2+3 x \right )}{2187}\) | \(44\) |
default | \(\frac {343}{13122 \left (2+3 x \right )^{6}}-\frac {1813}{3645 \left (2+3 x \right )^{5}}+\frac {10073}{2916 \left (2+3 x \right )^{4}}-\frac {66193}{6561 \left (2+3 x \right )^{3}}+\frac {7195}{729 \left (2+3 x \right )^{2}}-\frac {3700}{729 \left (2+3 x \right )}-\frac {1000 \ln \left (2+3 x \right )}{2187}\) | \(64\) |
parallelrisch | \(-\frac {466560000 \ln \left (\frac {2}{3}+x \right ) x^{6}+1866240000 \ln \left (\frac {2}{3}+x \right ) x^{5}-1153672389 x^{6}+3110400000 \ln \left (\frac {2}{3}+x \right ) x^{4}-2888417556 x^{5}+2764800000 \ln \left (\frac {2}{3}+x \right ) x^{3}-3055875660 x^{4}+1382400000 \ln \left (\frac {2}{3}+x \right ) x^{2}-1766895840 x^{3}+368640000 \ln \left (\frac {2}{3}+x \right ) x -568290960 x^{2}+40960000 \ln \left (\frac {2}{3}+x \right )-80335680 x}{1399680 \left (2+3 x \right )^{6}}\) | \(97\) |
meijerg | \(\frac {9 x \left (\frac {243}{32} x^{5}+\frac {243}{8} x^{4}+\frac {405}{8} x^{3}+45 x^{2}+\frac {45}{2} x +6\right )}{256 \left (1+\frac {3 x}{2}\right )^{6}}-\frac {9 x^{2} \left (\frac {81}{16} x^{4}+\frac {81}{4} x^{3}+\frac {135}{4} x^{2}+30 x +15\right )}{1280 \left (1+\frac {3 x}{2}\right )^{6}}-\frac {87 x^{3} \left (\frac {27}{8} x^{3}+\frac {27}{2} x^{2}+\frac {45}{2} x +20\right )}{2560 \left (1+\frac {3 x}{2}\right )^{6}}+\frac {179 x^{4} \left (\frac {9}{4} x^{2}+9 x +15\right )}{7680 \left (1+\frac {3 x}{2}\right )^{6}}+\frac {29 x^{5} \left (\frac {3 x}{2}+6\right )}{128 \left (1+\frac {3 x}{2}\right )^{6}}-\frac {25 x^{6}}{64 \left (1+\frac {3 x}{2}\right )^{6}}+\frac {25 x \left (\frac {250047}{32} x^{5}+\frac {147987}{8} x^{4}+\frac {161595}{8} x^{3}+11655 x^{2}+3465 x +420\right )}{15309 \left (1+\frac {3 x}{2}\right )^{6}}-\frac {1000 \ln \left (1+\frac {3 x}{2}\right )}{2187}\) | \(190\) |
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Time = 0.22 (sec) , antiderivative size = 97, normalized size of antiderivative = 1.26 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^7} \, dx=-\frac {53946000 \, x^{5} + 144852300 \, x^{4} + 158427540 \, x^{3} + 89062425 \, x^{2} + 20000 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (3 \, x + 2\right ) + 25975248 \, x + 3165082}{43740 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]
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Time = 0.08 (sec) , antiderivative size = 66, normalized size of antiderivative = 0.86 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^7} \, dx=- \frac {53946000 x^{5} + 144852300 x^{4} + 158427540 x^{3} + 89062425 x^{2} + 25975248 x + 3165082}{31886460 x^{6} + 127545840 x^{5} + 212576400 x^{4} + 188956800 x^{3} + 94478400 x^{2} + 25194240 x + 2799360} - \frac {1000 \log {\left (3 x + 2 \right )}}{2187} \]
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Time = 0.22 (sec) , antiderivative size = 68, normalized size of antiderivative = 0.88 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^7} \, dx=-\frac {53946000 \, x^{5} + 144852300 \, x^{4} + 158427540 \, x^{3} + 89062425 \, x^{2} + 25975248 \, x + 3165082}{43740 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} - \frac {1000}{2187} \, \log \left (3 \, x + 2\right ) \]
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Time = 0.26 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.57 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^7} \, dx=-\frac {53946000 \, x^{5} + 144852300 \, x^{4} + 158427540 \, x^{3} + 89062425 \, x^{2} + 25975248 \, x + 3165082}{43740 \, {\left (3 \, x + 2\right )}^{6}} - \frac {1000}{2187} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
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Time = 0.07 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.83 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^7} \, dx=-\frac {1000\,\ln \left (x+\frac {2}{3}\right )}{2187}-\frac {\frac {3700\,x^5}{2187}+\frac {9935\,x^4}{2187}+\frac {880153\,x^3}{177147}+\frac {1979165\,x^2}{708588}+\frac {2164604\,x}{2657205}+\frac {1582541}{15943230}}{x^6+4\,x^5+\frac {20\,x^4}{3}+\frac {160\,x^3}{27}+\frac {80\,x^2}{27}+\frac {64\,x}{81}+\frac {64}{729}} \]
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