Integrand size = 22, antiderivative size = 61 \[ \int \frac {(2+3 x)^7}{(1-2 x) (3+5 x)} \, dx=-\frac {1127138733 x}{1000000}-\frac {187738857 x^2}{200000}-\frac {7889751 x^3}{10000}-\frac {2006937 x^4}{4000}-\frac {99873 x^5}{500}-\frac {729 x^6}{20}-\frac {823543 \log (1-2 x)}{1408}+\frac {\log (3+5 x)}{859375} \]
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Time = 0.02 (sec) , antiderivative size = 61, 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 = {84} \[ \int \frac {(2+3 x)^7}{(1-2 x) (3+5 x)} \, dx=-\frac {729 x^6}{20}-\frac {99873 x^5}{500}-\frac {2006937 x^4}{4000}-\frac {7889751 x^3}{10000}-\frac {187738857 x^2}{200000}-\frac {1127138733 x}{1000000}-\frac {823543 \log (1-2 x)}{1408}+\frac {\log (5 x+3)}{859375} \]
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Rule 84
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {1127138733}{1000000}-\frac {187738857 x}{100000}-\frac {23669253 x^2}{10000}-\frac {2006937 x^3}{1000}-\frac {99873 x^4}{100}-\frac {2187 x^5}{10}-\frac {823543}{704 (-1+2 x)}+\frac {1}{171875 (3+5 x)}\right ) \, dx \\ & = -\frac {1127138733 x}{1000000}-\frac {187738857 x^2}{200000}-\frac {7889751 x^3}{10000}-\frac {2006937 x^4}{4000}-\frac {99873 x^5}{500}-\frac {729 x^6}{20}-\frac {823543 \log (1-2 x)}{1408}+\frac {\log (3+5 x)}{859375} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 58, normalized size of antiderivative = 0.95 \[ \int \frac {(2+3 x)^7}{(1-2 x) (3+5 x)} \, dx=-\frac {823543 \log (3-6 x)}{1408}+\frac {-165 \left (163998254+375712911 x+312898095 x^2+262991700 x^3+167244750 x^4+66582000 x^5+12150000 x^6\right )+64 \log (-3 (3+5 x))}{55000000} \]
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Time = 2.55 (sec) , antiderivative size = 42, normalized size of antiderivative = 0.69
method | result | size |
parallelrisch | \(-\frac {729 x^{6}}{20}-\frac {99873 x^{5}}{500}-\frac {2006937 x^{4}}{4000}-\frac {7889751 x^{3}}{10000}-\frac {187738857 x^{2}}{200000}-\frac {1127138733 x}{1000000}+\frac {\ln \left (x +\frac {3}{5}\right )}{859375}-\frac {823543 \ln \left (x -\frac {1}{2}\right )}{1408}\) | \(42\) |
default | \(-\frac {729 x^{6}}{20}-\frac {99873 x^{5}}{500}-\frac {2006937 x^{4}}{4000}-\frac {7889751 x^{3}}{10000}-\frac {187738857 x^{2}}{200000}-\frac {1127138733 x}{1000000}+\frac {\ln \left (3+5 x \right )}{859375}-\frac {823543 \ln \left (-1+2 x \right )}{1408}\) | \(46\) |
norman | \(-\frac {729 x^{6}}{20}-\frac {99873 x^{5}}{500}-\frac {2006937 x^{4}}{4000}-\frac {7889751 x^{3}}{10000}-\frac {187738857 x^{2}}{200000}-\frac {1127138733 x}{1000000}+\frac {\ln \left (3+5 x \right )}{859375}-\frac {823543 \ln \left (-1+2 x \right )}{1408}\) | \(46\) |
risch | \(-\frac {729 x^{6}}{20}-\frac {99873 x^{5}}{500}-\frac {2006937 x^{4}}{4000}-\frac {7889751 x^{3}}{10000}-\frac {187738857 x^{2}}{200000}-\frac {1127138733 x}{1000000}+\frac {\ln \left (3+5 x \right )}{859375}-\frac {823543 \ln \left (-1+2 x \right )}{1408}\) | \(46\) |
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Time = 0.22 (sec) , antiderivative size = 45, normalized size of antiderivative = 0.74 \[ \int \frac {(2+3 x)^7}{(1-2 x) (3+5 x)} \, dx=-\frac {729}{20} \, x^{6} - \frac {99873}{500} \, x^{5} - \frac {2006937}{4000} \, x^{4} - \frac {7889751}{10000} \, x^{3} - \frac {187738857}{200000} \, x^{2} - \frac {1127138733}{1000000} \, x + \frac {1}{859375} \, \log \left (5 \, x + 3\right ) - \frac {823543}{1408} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.07 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.92 \[ \int \frac {(2+3 x)^7}{(1-2 x) (3+5 x)} \, dx=- \frac {729 x^{6}}{20} - \frac {99873 x^{5}}{500} - \frac {2006937 x^{4}}{4000} - \frac {7889751 x^{3}}{10000} - \frac {187738857 x^{2}}{200000} - \frac {1127138733 x}{1000000} - \frac {823543 \log {\left (x - \frac {1}{2} \right )}}{1408} + \frac {\log {\left (x + \frac {3}{5} \right )}}{859375} \]
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Time = 0.19 (sec) , antiderivative size = 45, normalized size of antiderivative = 0.74 \[ \int \frac {(2+3 x)^7}{(1-2 x) (3+5 x)} \, dx=-\frac {729}{20} \, x^{6} - \frac {99873}{500} \, x^{5} - \frac {2006937}{4000} \, x^{4} - \frac {7889751}{10000} \, x^{3} - \frac {187738857}{200000} \, x^{2} - \frac {1127138733}{1000000} \, x + \frac {1}{859375} \, \log \left (5 \, x + 3\right ) - \frac {823543}{1408} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.26 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.77 \[ \int \frac {(2+3 x)^7}{(1-2 x) (3+5 x)} \, dx=-\frac {729}{20} \, x^{6} - \frac {99873}{500} \, x^{5} - \frac {2006937}{4000} \, x^{4} - \frac {7889751}{10000} \, x^{3} - \frac {187738857}{200000} \, x^{2} - \frac {1127138733}{1000000} \, x + \frac {1}{859375} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {823543}{1408} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
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Time = 0.06 (sec) , antiderivative size = 41, normalized size of antiderivative = 0.67 \[ \int \frac {(2+3 x)^7}{(1-2 x) (3+5 x)} \, dx=\frac {\ln \left (x+\frac {3}{5}\right )}{859375}-\frac {823543\,\ln \left (x-\frac {1}{2}\right )}{1408}-\frac {1127138733\,x}{1000000}-\frac {187738857\,x^2}{200000}-\frac {7889751\,x^3}{10000}-\frac {2006937\,x^4}{4000}-\frac {99873\,x^5}{500}-\frac {729\,x^6}{20} \]
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