Integrand size = 22, antiderivative size = 71 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^6} \, dx=-\frac {1000 x}{729}+\frac {343}{10935 (2+3 x)^5}-\frac {1813}{2916 (2+3 x)^4}+\frac {10073}{2187 (2+3 x)^3}-\frac {66193}{4374 (2+3 x)^2}+\frac {14390}{729 (2+3 x)}+\frac {3700}{729} \log (2+3 x) \]
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Time = 0.02 (sec) , antiderivative size = 71, 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} \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^6} \, dx=-\frac {1000 x}{729}+\frac {14390}{729 (3 x+2)}-\frac {66193}{4374 (3 x+2)^2}+\frac {10073}{2187 (3 x+2)^3}-\frac {1813}{2916 (3 x+2)^4}+\frac {343}{10935 (3 x+2)^5}+\frac {3700}{729} \log (3 x+2) \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {1000}{729}-\frac {343}{729 (2+3 x)^6}+\frac {1813}{243 (2+3 x)^5}-\frac {10073}{243 (2+3 x)^4}+\frac {66193}{729 (2+3 x)^3}-\frac {14390}{243 (2+3 x)^2}+\frac {3700}{243 (2+3 x)}\right ) \, dx \\ & = -\frac {1000 x}{729}+\frac {343}{10935 (2+3 x)^5}-\frac {1813}{2916 (2+3 x)^4}+\frac {10073}{2187 (2+3 x)^3}-\frac {66193}{4374 (2+3 x)^2}+\frac {14390}{729 (2+3 x)}+\frac {3700}{729} \log (2+3 x) \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.79 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^6} \, dx=\frac {7991782+49872855 x+109363320 x^2+82222290 x^3-27264600 x^4-58320000 x^5-14580000 x^6+222000 (2+3 x)^5 \log (2+3 x)}{43740 (2+3 x)^5} \]
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Time = 2.44 (sec) , antiderivative size = 42, normalized size of antiderivative = 0.59
method | result | size |
risch | \(-\frac {1000 x}{729}+\frac {\frac {14390}{9} x^{4}+\frac {624527}{162} x^{3}+\frac {847574}{243} x^{2}+\frac {4092857}{2916} x +\frac {515099}{2430}}{\left (2+3 x \right )^{5}}+\frac {3700 \ln \left (2+3 x \right )}{729}\) | \(42\) |
norman | \(\frac {\frac {34390}{9} x^{4}+\frac {140503}{18} x^{3}+\frac {1567574}{243} x^{2}+\frac {7164857}{2916} x -\frac {1000}{3} x^{6}+\frac {7835891}{21870}}{\left (2+3 x \right )^{5}}+\frac {3700 \ln \left (2+3 x \right )}{729}\) | \(43\) |
default | \(-\frac {1000 x}{729}+\frac {343}{10935 \left (2+3 x \right )^{5}}-\frac {1813}{2916 \left (2+3 x \right )^{4}}+\frac {10073}{2187 \left (2+3 x \right )^{3}}-\frac {66193}{4374 \left (2+3 x \right )^{2}}+\frac {14390}{729 \left (2+3 x \right )}+\frac {3700 \ln \left (2+3 x \right )}{729}\) | \(58\) |
parallelrisch | \(\frac {287712000 \ln \left (\frac {2}{3}+x \right ) x^{5}-77760000 x^{6}+959040000 \ln \left (\frac {2}{3}+x \right ) x^{4}-634707171 x^{5}+1278720000 \ln \left (\frac {2}{3}+x \right ) x^{3}-1224301770 x^{4}+852480000 \ln \left (\frac {2}{3}+x \right ) x^{2}-1000001880 x^{3}+284160000 \ln \left (\frac {2}{3}+x \right ) x -375742800 x^{2}+37888000 \ln \left (\frac {2}{3}+x \right )-53682720 x}{233280 \left (2+3 x \right )^{5}}\) | \(88\) |
meijerg | \(\frac {27 x \left (\frac {81}{16} x^{4}+\frac {135}{8} x^{3}+\frac {45}{2} x^{2}+15 x +5\right )}{320 \left (1+\frac {3 x}{2}\right )^{5}}-\frac {27 x^{2} \left (\frac {27}{8} x^{3}+\frac {45}{4} x^{2}+15 x +10\right )}{1280 \left (1+\frac {3 x}{2}\right )^{5}}-\frac {87 x^{3} \left (\frac {9}{4} x^{2}+\frac {15}{2} x +10\right )}{640 \left (1+\frac {3 x}{2}\right )^{5}}+\frac {179 x^{4} \left (\frac {3 x}{2}+5\right )}{1280 \left (1+\frac {3 x}{2}\right )^{5}}+\frac {87 x^{5}}{32 \left (1+\frac {3 x}{2}\right )^{5}}+\frac {5 x \left (\frac {11097}{16} x^{4}+\frac {10395}{8} x^{3}+\frac {2115}{2} x^{2}+405 x +60\right )}{486 \left (1+\frac {3 x}{2}\right )^{5}}+\frac {3700 \ln \left (1+\frac {3 x}{2}\right )}{729}-\frac {100 x \left (\frac {8505}{16} x^{5}+\frac {77679}{16} x^{4}+\frac {72765}{8} x^{3}+\frac {14805}{2} x^{2}+2835 x +420\right )}{5103 \left (1+\frac {3 x}{2}\right )^{5}}\) | \(183\) |
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Time = 0.21 (sec) , antiderivative size = 92, normalized size of antiderivative = 1.30 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^6} \, dx=-\frac {4860000 \, x^{6} + 16200000 \, x^{5} - 1711800 \, x^{4} - 41807430 \, x^{3} - 46054440 \, x^{2} - 74000 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (3 \, x + 2\right ) - 19824285 \, x - 3090594}{14580 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
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Time = 0.07 (sec) , antiderivative size = 61, normalized size of antiderivative = 0.86 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^6} \, dx=- \frac {1000 x}{729} - \frac {- 23311800 x^{4} - 56207430 x^{3} - 50854440 x^{2} - 20464285 x - 3090594}{3542940 x^{5} + 11809800 x^{4} + 15746400 x^{3} + 10497600 x^{2} + 3499200 x + 466560} + \frac {3700 \log {\left (3 x + 2 \right )}}{729} \]
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Time = 0.21 (sec) , antiderivative size = 61, normalized size of antiderivative = 0.86 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^6} \, dx=-\frac {1000}{729} \, x + \frac {23311800 \, x^{4} + 56207430 \, x^{3} + 50854440 \, x^{2} + 20464285 \, x + 3090594}{14580 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} + \frac {3700}{729} \, \log \left (3 \, x + 2\right ) \]
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Time = 0.28 (sec) , antiderivative size = 42, normalized size of antiderivative = 0.59 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^6} \, dx=-\frac {1000}{729} \, x + \frac {23311800 \, x^{4} + 56207430 \, x^{3} + 50854440 \, x^{2} + 20464285 \, x + 3090594}{14580 \, {\left (3 \, x + 2\right )}^{5}} + \frac {3700}{729} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
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Time = 1.25 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.79 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^6} \, dx=\frac {3700\,\ln \left (x+\frac {2}{3}\right )}{729}-\frac {1000\,x}{729}+\frac {\frac {14390\,x^4}{2187}+\frac {624527\,x^3}{39366}+\frac {847574\,x^2}{59049}+\frac {4092857\,x}{708588}+\frac {515099}{590490}}{x^5+\frac {10\,x^4}{3}+\frac {40\,x^3}{9}+\frac {80\,x^2}{27}+\frac {80\,x}{81}+\frac {32}{243}} \]
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