Integrand size = 20, antiderivative size = 58 \[ \int \frac {(2+3 x)^6 (3+5 x)}{1-2 x} \, dx=-\frac {1269563 x}{128}-\frac {1138491 x^2}{128}-\frac {279657 x^3}{32}-\frac {458811 x^4}{64}-\frac {169371 x^5}{40}-\frac {12393 x^6}{8}-\frac {3645 x^7}{14}-\frac {1294139}{256} \log (1-2 x) \]
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Time = 0.02 (sec) , antiderivative size = 58, 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} \[ \int \frac {(2+3 x)^6 (3+5 x)}{1-2 x} \, dx=-\frac {3645 x^7}{14}-\frac {12393 x^6}{8}-\frac {169371 x^5}{40}-\frac {458811 x^4}{64}-\frac {279657 x^3}{32}-\frac {1138491 x^2}{128}-\frac {1269563 x}{128}-\frac {1294139}{256} \log (1-2 x) \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {1269563}{128}-\frac {1138491 x}{64}-\frac {838971 x^2}{32}-\frac {458811 x^3}{16}-\frac {169371 x^4}{8}-\frac {37179 x^5}{4}-\frac {3645 x^6}{2}-\frac {1294139}{128 (-1+2 x)}\right ) \, dx \\ & = -\frac {1269563 x}{128}-\frac {1138491 x^2}{128}-\frac {279657 x^3}{32}-\frac {458811 x^4}{64}-\frac {169371 x^5}{40}-\frac {12393 x^6}{8}-\frac {3645 x^7}{14}-\frac {1294139}{256} \log (1-2 x) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.81 \[ \int \frac {(2+3 x)^6 (3+5 x)}{1-2 x} \, dx=\frac {318326353-355477640 x-318777480 x^2-313215840 x^3-256934160 x^4-151756416 x^5-55520640 x^6-9331200 x^7-181179460 \log (1-2 x)}{35840} \]
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Time = 2.50 (sec) , antiderivative size = 41, normalized size of antiderivative = 0.71
method | result | size |
parallelrisch | \(-\frac {3645 x^{7}}{14}-\frac {12393 x^{6}}{8}-\frac {169371 x^{5}}{40}-\frac {458811 x^{4}}{64}-\frac {279657 x^{3}}{32}-\frac {1138491 x^{2}}{128}-\frac {1269563 x}{128}-\frac {1294139 \ln \left (x -\frac {1}{2}\right )}{256}\) | \(41\) |
default | \(-\frac {3645 x^{7}}{14}-\frac {12393 x^{6}}{8}-\frac {169371 x^{5}}{40}-\frac {458811 x^{4}}{64}-\frac {279657 x^{3}}{32}-\frac {1138491 x^{2}}{128}-\frac {1269563 x}{128}-\frac {1294139 \ln \left (-1+2 x \right )}{256}\) | \(43\) |
norman | \(-\frac {3645 x^{7}}{14}-\frac {12393 x^{6}}{8}-\frac {169371 x^{5}}{40}-\frac {458811 x^{4}}{64}-\frac {279657 x^{3}}{32}-\frac {1138491 x^{2}}{128}-\frac {1269563 x}{128}-\frac {1294139 \ln \left (-1+2 x \right )}{256}\) | \(43\) |
risch | \(-\frac {3645 x^{7}}{14}-\frac {12393 x^{6}}{8}-\frac {169371 x^{5}}{40}-\frac {458811 x^{4}}{64}-\frac {279657 x^{3}}{32}-\frac {1138491 x^{2}}{128}-\frac {1269563 x}{128}-\frac {1294139 \ln \left (-1+2 x \right )}{256}\) | \(43\) |
meijerg | \(-\frac {1294139 \ln \left (1-2 x \right )}{256}-1024 x -390 x \left (6 x +6\right )-\frac {495 x \left (16 x^{2}+12 x +12\right )}{2}-\frac {603 x \left (120 x^{3}+80 x^{2}+60 x +60\right )}{16}-\frac {1377 x \left (192 x^{4}+120 x^{3}+80 x^{2}+60 x +60\right )}{80}-\frac {5589 x \left (2240 x^{5}+1344 x^{4}+840 x^{3}+560 x^{2}+420 x +420\right )}{8960}-\frac {243 x \left (7680 x^{6}+4480 x^{5}+2688 x^{4}+1680 x^{3}+1120 x^{2}+840 x +840\right )}{7168}\) | \(136\) |
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Time = 0.22 (sec) , antiderivative size = 42, normalized size of antiderivative = 0.72 \[ \int \frac {(2+3 x)^6 (3+5 x)}{1-2 x} \, dx=-\frac {3645}{14} \, x^{7} - \frac {12393}{8} \, x^{6} - \frac {169371}{40} \, x^{5} - \frac {458811}{64} \, x^{4} - \frac {279657}{32} \, x^{3} - \frac {1138491}{128} \, x^{2} - \frac {1269563}{128} \, x - \frac {1294139}{256} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.05 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.97 \[ \int \frac {(2+3 x)^6 (3+5 x)}{1-2 x} \, dx=- \frac {3645 x^{7}}{14} - \frac {12393 x^{6}}{8} - \frac {169371 x^{5}}{40} - \frac {458811 x^{4}}{64} - \frac {279657 x^{3}}{32} - \frac {1138491 x^{2}}{128} - \frac {1269563 x}{128} - \frac {1294139 \log {\left (2 x - 1 \right )}}{256} \]
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Time = 0.20 (sec) , antiderivative size = 42, normalized size of antiderivative = 0.72 \[ \int \frac {(2+3 x)^6 (3+5 x)}{1-2 x} \, dx=-\frac {3645}{14} \, x^{7} - \frac {12393}{8} \, x^{6} - \frac {169371}{40} \, x^{5} - \frac {458811}{64} \, x^{4} - \frac {279657}{32} \, x^{3} - \frac {1138491}{128} \, x^{2} - \frac {1269563}{128} \, x - \frac {1294139}{256} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.31 (sec) , antiderivative size = 43, normalized size of antiderivative = 0.74 \[ \int \frac {(2+3 x)^6 (3+5 x)}{1-2 x} \, dx=-\frac {3645}{14} \, x^{7} - \frac {12393}{8} \, x^{6} - \frac {169371}{40} \, x^{5} - \frac {458811}{64} \, x^{4} - \frac {279657}{32} \, x^{3} - \frac {1138491}{128} \, x^{2} - \frac {1269563}{128} \, x - \frac {1294139}{256} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
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Time = 0.04 (sec) , antiderivative size = 40, normalized size of antiderivative = 0.69 \[ \int \frac {(2+3 x)^6 (3+5 x)}{1-2 x} \, dx=-\frac {1269563\,x}{128}-\frac {1294139\,\ln \left (x-\frac {1}{2}\right )}{256}-\frac {1138491\,x^2}{128}-\frac {279657\,x^3}{32}-\frac {458811\,x^4}{64}-\frac {169371\,x^5}{40}-\frac {12393\,x^6}{8}-\frac {3645\,x^7}{14} \]
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