Integrand size = 22, antiderivative size = 65 \[ \int \frac {(2+3 x)^7}{(1-2 x)^2 (3+5 x)} \, dx=\frac {823543}{1408 (1-2 x)}+\frac {370109547 x}{200000}+\frac {18237069 x^2}{20000}+\frac {853659 x^3}{2000}+\frac {13851 x^4}{100}+\frac {2187 x^5}{100}+\frac {5764801 \log (1-2 x)}{3872}+\frac {\log (3+5 x)}{1890625} \]
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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} \[ \int \frac {(2+3 x)^7}{(1-2 x)^2 (3+5 x)} \, dx=\frac {2187 x^5}{100}+\frac {13851 x^4}{100}+\frac {853659 x^3}{2000}+\frac {18237069 x^2}{20000}+\frac {370109547 x}{200000}+\frac {823543}{1408 (1-2 x)}+\frac {5764801 \log (1-2 x)}{3872}+\frac {\log (5 x+3)}{1890625} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {370109547}{200000}+\frac {18237069 x}{10000}+\frac {2560977 x^2}{2000}+\frac {13851 x^3}{25}+\frac {2187 x^4}{20}+\frac {823543}{704 (-1+2 x)^2}+\frac {5764801}{1936 (-1+2 x)}+\frac {1}{378125 (3+5 x)}\right ) \, dx \\ & = \frac {823543}{1408 (1-2 x)}+\frac {370109547 x}{200000}+\frac {18237069 x^2}{20000}+\frac {853659 x^3}{2000}+\frac {13851 x^4}{100}+\frac {2187 x^5}{100}+\frac {5764801 \log (1-2 x)}{3872}+\frac {\log (3+5 x)}{1890625} \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 60, normalized size of antiderivative = 0.92 \[ \int \frac {(2+3 x)^7}{(1-2 x)^2 (3+5 x)} \, dx=\frac {\frac {11 \left (-158719988357-14798867886 x+306816622200 x^2+153656514000 x^3+78666390000 x^4+28066500000 x^5+4811400000 x^6\right )}{-1+2 x}+1801500312500 \log (5-10 x)+640 \log (3+5 x)}{1210000000} \]
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Time = 0.87 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.74
method | result | size |
risch | \(\frac {2187 x^{5}}{100}+\frac {13851 x^{4}}{100}+\frac {853659 x^{3}}{2000}+\frac {18237069 x^{2}}{20000}+\frac {370109547 x}{200000}-\frac {823543}{2816 \left (x -\frac {1}{2}\right )}+\frac {5764801 \ln \left (-1+2 x \right )}{3872}+\frac {\ln \left (3+5 x \right )}{1890625}\) | \(48\) |
default | \(\frac {2187 x^{5}}{100}+\frac {13851 x^{4}}{100}+\frac {853659 x^{3}}{2000}+\frac {18237069 x^{2}}{20000}+\frac {370109547 x}{200000}+\frac {\ln \left (3+5 x \right )}{1890625}-\frac {823543}{1408 \left (-1+2 x \right )}+\frac {5764801 \ln \left (-1+2 x \right )}{3872}\) | \(50\) |
norman | \(\frac {-\frac {1661194223}{550000} x +\frac {139462101}{50000} x^{2}+\frac {6984387}{5000} x^{3}+\frac {715149}{1000} x^{4}+\frac {5103}{20} x^{5}+\frac {2187}{50} x^{6}}{-1+2 x}+\frac {5764801 \ln \left (-1+2 x \right )}{3872}+\frac {\ln \left (3+5 x \right )}{1890625}\) | \(55\) |
parallelrisch | \(\frac {2646270000 x^{6}+15436575000 x^{5}+43266514500 x^{4}+84511082700 x^{3}+64 \ln \left (x +\frac {3}{5}\right ) x +180150031250 \ln \left (x -\frac {1}{2}\right ) x +168749142210 x^{2}-32 \ln \left (x +\frac {3}{5}\right )-90075015625 \ln \left (x -\frac {1}{2}\right )-182731364530 x}{-60500000+121000000 x}\) | \(65\) |
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Time = 0.22 (sec) , antiderivative size = 65, normalized size of antiderivative = 1.00 \[ \int \frac {(2+3 x)^7}{(1-2 x)^2 (3+5 x)} \, dx=\frac {10585080000 \, x^{6} + 61746300000 \, x^{5} + 173066058000 \, x^{4} + 338044330800 \, x^{3} + 674996568840 \, x^{2} + 128 \, {\left (2 \, x - 1\right )} \log \left (5 \, x + 3\right ) + 360300062500 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 447832551870 \, x - 141546453125}{242000000 \, {\left (2 \, x - 1\right )}} \]
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Time = 0.07 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.86 \[ \int \frac {(2+3 x)^7}{(1-2 x)^2 (3+5 x)} \, dx=\frac {2187 x^{5}}{100} + \frac {13851 x^{4}}{100} + \frac {853659 x^{3}}{2000} + \frac {18237069 x^{2}}{20000} + \frac {370109547 x}{200000} + \frac {5764801 \log {\left (x - \frac {1}{2} \right )}}{3872} + \frac {\log {\left (x + \frac {3}{5} \right )}}{1890625} - \frac {823543}{2816 x - 1408} \]
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Time = 0.20 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.75 \[ \int \frac {(2+3 x)^7}{(1-2 x)^2 (3+5 x)} \, dx=\frac {2187}{100} \, x^{5} + \frac {13851}{100} \, x^{4} + \frac {853659}{2000} \, x^{3} + \frac {18237069}{20000} \, x^{2} + \frac {370109547}{200000} \, x - \frac {823543}{1408 \, {\left (2 \, x - 1\right )}} + \frac {1}{1890625} \, \log \left (5 \, x + 3\right ) + \frac {5764801}{3872} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.29 (sec) , antiderivative size = 90, normalized size of antiderivative = 1.38 \[ \int \frac {(2+3 x)^7}{(1-2 x)^2 (3+5 x)} \, dx=\frac {27}{400000} \, {\left (2 \, x - 1\right )}^{5} {\left (\frac {178875}{2 \, x - 1} + \frac {1404675}{{\left (2 \, x - 1\right )}^{2}} + \frac {6619260}{{\left (2 \, x - 1\right )}^{3}} + \frac {23397131}{{\left (2 \, x - 1\right )}^{4}} + 10125\right )} - \frac {823543}{1408 \, {\left (2 \, x - 1\right )}} - \frac {744421617}{500000} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) + \frac {1}{1890625} \, \log \left ({\left | -\frac {11}{2 \, x - 1} - 5 \right |}\right ) \]
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Time = 1.30 (sec) , antiderivative size = 45, normalized size of antiderivative = 0.69 \[ \int \frac {(2+3 x)^7}{(1-2 x)^2 (3+5 x)} \, dx=\frac {370109547\,x}{200000}+\frac {5764801\,\ln \left (x-\frac {1}{2}\right )}{3872}+\frac {\ln \left (x+\frac {3}{5}\right )}{1890625}-\frac {823543}{2816\,\left (x-\frac {1}{2}\right )}+\frac {18237069\,x^2}{20000}+\frac {853659\,x^3}{2000}+\frac {13851\,x^4}{100}+\frac {2187\,x^5}{100} \]
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