Integrand size = 22, antiderivative size = 65 \[ \int \frac {(2+3 x)^6 (3+5 x)^2}{1-2 x} \, dx=-\frac {14088073 x}{256}-\frac {13178761 x^2}{256}-\frac {3575427 x^3}{64}-\frac {6947721 x^4}{128}-\frac {3310281 x^5}{80}-\frac {356643 x^6}{16}-\frac {207765 x^7}{28}-\frac {18225 x^8}{16}-\frac {14235529}{512} \log (1-2 x) \]
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Time = 0.02 (sec) , antiderivative size = 65, 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} \[ \int \frac {(2+3 x)^6 (3+5 x)^2}{1-2 x} \, dx=-\frac {18225 x^8}{16}-\frac {207765 x^7}{28}-\frac {356643 x^6}{16}-\frac {3310281 x^5}{80}-\frac {6947721 x^4}{128}-\frac {3575427 x^3}{64}-\frac {13178761 x^2}{256}-\frac {14088073 x}{256}-\frac {14235529}{512} \log (1-2 x) \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {14088073}{256}-\frac {13178761 x}{128}-\frac {10726281 x^2}{64}-\frac {6947721 x^3}{32}-\frac {3310281 x^4}{16}-\frac {1069929 x^5}{8}-\frac {207765 x^6}{4}-\frac {18225 x^7}{2}-\frac {14235529}{256 (-1+2 x)}\right ) \, dx \\ & = -\frac {14088073 x}{256}-\frac {13178761 x^2}{256}-\frac {3575427 x^3}{64}-\frac {6947721 x^4}{128}-\frac {3310281 x^5}{80}-\frac {356643 x^6}{16}-\frac {207765 x^7}{28}-\frac {18225 x^8}{16}-\frac {14235529}{512} \log (1-2 x) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 52, normalized size of antiderivative = 0.80 \[ \int \frac {(2+3 x)^6 (3+5 x)^2}{1-2 x} \, dx=\frac {7521401241-7889320880 x-7380106160 x^2-8008956480 x^3-7781447520 x^4-5932023552 x^5-3195521280 x^6-1063756800 x^7-163296000 x^8-3985948120 \log (1-2 x)}{143360} \]
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Time = 0.84 (sec) , antiderivative size = 46, normalized size of antiderivative = 0.71
method | result | size |
parallelrisch | \(-\frac {18225 x^{8}}{16}-\frac {207765 x^{7}}{28}-\frac {356643 x^{6}}{16}-\frac {3310281 x^{5}}{80}-\frac {6947721 x^{4}}{128}-\frac {3575427 x^{3}}{64}-\frac {13178761 x^{2}}{256}-\frac {14088073 x}{256}-\frac {14235529 \ln \left (x -\frac {1}{2}\right )}{512}\) | \(46\) |
default | \(-\frac {18225 x^{8}}{16}-\frac {207765 x^{7}}{28}-\frac {356643 x^{6}}{16}-\frac {3310281 x^{5}}{80}-\frac {6947721 x^{4}}{128}-\frac {3575427 x^{3}}{64}-\frac {13178761 x^{2}}{256}-\frac {14088073 x}{256}-\frac {14235529 \ln \left (-1+2 x \right )}{512}\) | \(48\) |
norman | \(-\frac {18225 x^{8}}{16}-\frac {207765 x^{7}}{28}-\frac {356643 x^{6}}{16}-\frac {3310281 x^{5}}{80}-\frac {6947721 x^{4}}{128}-\frac {3575427 x^{3}}{64}-\frac {13178761 x^{2}}{256}-\frac {14088073 x}{256}-\frac {14235529 \ln \left (-1+2 x \right )}{512}\) | \(48\) |
risch | \(-\frac {18225 x^{8}}{16}-\frac {207765 x^{7}}{28}-\frac {356643 x^{6}}{16}-\frac {3310281 x^{5}}{80}-\frac {6947721 x^{4}}{128}-\frac {3575427 x^{3}}{64}-\frac {13178761 x^{2}}{256}-\frac {14088073 x}{256}-\frac {14235529 \ln \left (-1+2 x \right )}{512}\) | \(48\) |
meijerg | \(-\frac {14235529 \ln \left (1-2 x \right )}{512}-3552 x -\frac {4790 x \left (6 x +6\right )}{3}-1230 x \left (16 x^{2}+12 x +12\right )-\frac {3789 x \left (120 x^{3}+80 x^{2}+60 x +60\right )}{16}-\frac {23337 x \left (192 x^{4}+120 x^{3}+80 x^{2}+60 x +60\right )}{160}-\frac {71847 x \left (2240 x^{5}+1344 x^{4}+840 x^{3}+560 x^{2}+420 x +420\right )}{8960}-\frac {3159 x \left (7680 x^{6}+4480 x^{5}+2688 x^{4}+1680 x^{3}+1120 x^{2}+840 x +840\right )}{3584}-\frac {405 x \left (40320 x^{7}+23040 x^{6}+13440 x^{5}+8064 x^{4}+5040 x^{3}+3360 x^{2}+2520 x +2520\right )}{14336}\) | \(174\) |
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Time = 0.22 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.72 \[ \int \frac {(2+3 x)^6 (3+5 x)^2}{1-2 x} \, dx=-\frac {18225}{16} \, x^{8} - \frac {207765}{28} \, x^{7} - \frac {356643}{16} \, x^{6} - \frac {3310281}{80} \, x^{5} - \frac {6947721}{128} \, x^{4} - \frac {3575427}{64} \, x^{3} - \frac {13178761}{256} \, x^{2} - \frac {14088073}{256} \, x - \frac {14235529}{512} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.05 (sec) , antiderivative size = 63, normalized size of antiderivative = 0.97 \[ \int \frac {(2+3 x)^6 (3+5 x)^2}{1-2 x} \, dx=- \frac {18225 x^{8}}{16} - \frac {207765 x^{7}}{28} - \frac {356643 x^{6}}{16} - \frac {3310281 x^{5}}{80} - \frac {6947721 x^{4}}{128} - \frac {3575427 x^{3}}{64} - \frac {13178761 x^{2}}{256} - \frac {14088073 x}{256} - \frac {14235529 \log {\left (2 x - 1 \right )}}{512} \]
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Time = 0.22 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.72 \[ \int \frac {(2+3 x)^6 (3+5 x)^2}{1-2 x} \, dx=-\frac {18225}{16} \, x^{8} - \frac {207765}{28} \, x^{7} - \frac {356643}{16} \, x^{6} - \frac {3310281}{80} \, x^{5} - \frac {6947721}{128} \, x^{4} - \frac {3575427}{64} \, x^{3} - \frac {13178761}{256} \, x^{2} - \frac {14088073}{256} \, x - \frac {14235529}{512} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.26 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.74 \[ \int \frac {(2+3 x)^6 (3+5 x)^2}{1-2 x} \, dx=-\frac {18225}{16} \, x^{8} - \frac {207765}{28} \, x^{7} - \frac {356643}{16} \, x^{6} - \frac {3310281}{80} \, x^{5} - \frac {6947721}{128} \, x^{4} - \frac {3575427}{64} \, x^{3} - \frac {13178761}{256} \, x^{2} - \frac {14088073}{256} \, x - \frac {14235529}{512} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
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Time = 0.04 (sec) , antiderivative size = 45, normalized size of antiderivative = 0.69 \[ \int \frac {(2+3 x)^6 (3+5 x)^2}{1-2 x} \, dx=-\frac {14088073\,x}{256}-\frac {14235529\,\ln \left (x-\frac {1}{2}\right )}{512}-\frac {13178761\,x^2}{256}-\frac {3575427\,x^3}{64}-\frac {6947721\,x^4}{128}-\frac {3310281\,x^5}{80}-\frac {356643\,x^6}{16}-\frac {207765\,x^7}{28}-\frac {18225\,x^8}{16} \]
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