Integrand size = 20, antiderivative size = 51 \[ \int \frac {(2+3 x)^5 (3+5 x)}{1-2 x} \, dx=-\frac {178733 x}{64}-\frac {150573 x^2}{64}-\frac {32271 x^3}{16}-\frac {42093 x^4}{32}-\frac {10773 x^5}{20}-\frac {405 x^6}{4}-\frac {184877}{128} \log (1-2 x) \]
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Time = 0.01 (sec) , antiderivative size = 51, 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} \[ \int \frac {(2+3 x)^5 (3+5 x)}{1-2 x} \, dx=-\frac {405 x^6}{4}-\frac {10773 x^5}{20}-\frac {42093 x^4}{32}-\frac {32271 x^3}{16}-\frac {150573 x^2}{64}-\frac {178733 x}{64}-\frac {184877}{128} \log (1-2 x) \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {178733}{64}-\frac {150573 x}{32}-\frac {96813 x^2}{16}-\frac {42093 x^3}{8}-\frac {10773 x^4}{4}-\frac {1215 x^5}{2}-\frac {184877}{64 (-1+2 x)}\right ) \, dx \\ & = -\frac {178733 x}{64}-\frac {150573 x^2}{64}-\frac {32271 x^3}{16}-\frac {42093 x^4}{32}-\frac {10773 x^5}{20}-\frac {405 x^6}{4}-\frac {184877}{128} \log (1-2 x) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 42, normalized size of antiderivative = 0.82 \[ \int \frac {(2+3 x)^5 (3+5 x)}{1-2 x} \, dx=\frac {5983417-7149320 x-6022920 x^2-5163360 x^3-3367440 x^4-1378944 x^5-259200 x^6-3697540 \log (1-2 x)}{2560} \]
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Time = 2.51 (sec) , antiderivative size = 36, normalized size of antiderivative = 0.71
method | result | size |
parallelrisch | \(-\frac {405 x^{6}}{4}-\frac {10773 x^{5}}{20}-\frac {42093 x^{4}}{32}-\frac {32271 x^{3}}{16}-\frac {150573 x^{2}}{64}-\frac {178733 x}{64}-\frac {184877 \ln \left (x -\frac {1}{2}\right )}{128}\) | \(36\) |
default | \(-\frac {405 x^{6}}{4}-\frac {10773 x^{5}}{20}-\frac {42093 x^{4}}{32}-\frac {32271 x^{3}}{16}-\frac {150573 x^{2}}{64}-\frac {178733 x}{64}-\frac {184877 \ln \left (-1+2 x \right )}{128}\) | \(38\) |
norman | \(-\frac {405 x^{6}}{4}-\frac {10773 x^{5}}{20}-\frac {42093 x^{4}}{32}-\frac {32271 x^{3}}{16}-\frac {150573 x^{2}}{64}-\frac {178733 x}{64}-\frac {184877 \ln \left (-1+2 x \right )}{128}\) | \(38\) |
risch | \(-\frac {405 x^{6}}{4}-\frac {10773 x^{5}}{20}-\frac {42093 x^{4}}{32}-\frac {32271 x^{3}}{16}-\frac {150573 x^{2}}{64}-\frac {178733 x}{64}-\frac {184877 \ln \left (-1+2 x \right )}{128}\) | \(38\) |
meijerg | \(-\frac {184877 \ln \left (1-2 x \right )}{128}-440 x -140 x \left (6 x +6\right )-\frac {285 x \left (16 x^{2}+12 x +12\right )}{4}-\frac {261 x \left (120 x^{3}+80 x^{2}+60 x +60\right )}{32}-\frac {1593 x \left (192 x^{4}+120 x^{3}+80 x^{2}+60 x +60\right )}{640}-\frac {81 x \left (2240 x^{5}+1344 x^{4}+840 x^{3}+560 x^{2}+420 x +420\right )}{1792}\) | \(103\) |
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Time = 0.22 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.73 \[ \int \frac {(2+3 x)^5 (3+5 x)}{1-2 x} \, dx=-\frac {405}{4} \, x^{6} - \frac {10773}{20} \, x^{5} - \frac {42093}{32} \, x^{4} - \frac {32271}{16} \, x^{3} - \frac {150573}{64} \, x^{2} - \frac {178733}{64} \, x - \frac {184877}{128} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.05 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.96 \[ \int \frac {(2+3 x)^5 (3+5 x)}{1-2 x} \, dx=- \frac {405 x^{6}}{4} - \frac {10773 x^{5}}{20} - \frac {42093 x^{4}}{32} - \frac {32271 x^{3}}{16} - \frac {150573 x^{2}}{64} - \frac {178733 x}{64} - \frac {184877 \log {\left (2 x - 1 \right )}}{128} \]
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Time = 0.20 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.73 \[ \int \frac {(2+3 x)^5 (3+5 x)}{1-2 x} \, dx=-\frac {405}{4} \, x^{6} - \frac {10773}{20} \, x^{5} - \frac {42093}{32} \, x^{4} - \frac {32271}{16} \, x^{3} - \frac {150573}{64} \, x^{2} - \frac {178733}{64} \, x - \frac {184877}{128} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.27 (sec) , antiderivative size = 38, normalized size of antiderivative = 0.75 \[ \int \frac {(2+3 x)^5 (3+5 x)}{1-2 x} \, dx=-\frac {405}{4} \, x^{6} - \frac {10773}{20} \, x^{5} - \frac {42093}{32} \, x^{4} - \frac {32271}{16} \, x^{3} - \frac {150573}{64} \, x^{2} - \frac {178733}{64} \, x - \frac {184877}{128} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
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Time = 0.03 (sec) , antiderivative size = 35, normalized size of antiderivative = 0.69 \[ \int \frac {(2+3 x)^5 (3+5 x)}{1-2 x} \, dx=-\frac {178733\,x}{64}-\frac {184877\,\ln \left (x-\frac {1}{2}\right )}{128}-\frac {150573\,x^2}{64}-\frac {32271\,x^3}{16}-\frac {42093\,x^4}{32}-\frac {10773\,x^5}{20}-\frac {405\,x^6}{4} \]
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