Integrand size = 22, antiderivative size = 40 \[ \int \frac {(2+3 x)^4}{(1-2 x) (3+5 x)} \, dx=-\frac {21951 x}{1000}-\frac {2079 x^2}{200}-\frac {27 x^3}{10}-\frac {2401}{176} \log (1-2 x)+\frac {\log (3+5 x)}{6875} \]
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Time = 0.01 (sec) , antiderivative size = 40, 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} \[ \int \frac {(2+3 x)^4}{(1-2 x) (3+5 x)} \, dx=-\frac {27 x^3}{10}-\frac {2079 x^2}{200}-\frac {21951 x}{1000}-\frac {2401}{176} \log (1-2 x)+\frac {\log (5 x+3)}{6875} \]
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Rule 84
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {21951}{1000}-\frac {2079 x}{100}-\frac {81 x^2}{10}-\frac {2401}{88 (-1+2 x)}+\frac {1}{1375 (3+5 x)}\right ) \, dx \\ & = -\frac {21951 x}{1000}-\frac {2079 x^2}{200}-\frac {27 x^3}{10}-\frac {2401}{176} \log (1-2 x)+\frac {\log (3+5 x)}{6875} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.08 \[ \int \frac {(2+3 x)^4}{(1-2 x) (3+5 x)} \, dx=-\frac {2401}{176} \log (3-6 x)+\frac {-55 \left (10814+21951 x+10395 x^2+2700 x^3\right )+8 \log (-3 (3+5 x))}{55000} \]
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Time = 2.55 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.68
method | result | size |
parallelrisch | \(-\frac {27 x^{3}}{10}-\frac {2079 x^{2}}{200}-\frac {21951 x}{1000}+\frac {\ln \left (x +\frac {3}{5}\right )}{6875}-\frac {2401 \ln \left (x -\frac {1}{2}\right )}{176}\) | \(27\) |
default | \(-\frac {27 x^{3}}{10}-\frac {2079 x^{2}}{200}-\frac {21951 x}{1000}+\frac {\ln \left (3+5 x \right )}{6875}-\frac {2401 \ln \left (-1+2 x \right )}{176}\) | \(31\) |
norman | \(-\frac {27 x^{3}}{10}-\frac {2079 x^{2}}{200}-\frac {21951 x}{1000}+\frac {\ln \left (3+5 x \right )}{6875}-\frac {2401 \ln \left (-1+2 x \right )}{176}\) | \(31\) |
risch | \(-\frac {27 x^{3}}{10}-\frac {2079 x^{2}}{200}-\frac {21951 x}{1000}+\frac {\ln \left (3+5 x \right )}{6875}-\frac {2401 \ln \left (-1+2 x \right )}{176}\) | \(31\) |
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Time = 0.22 (sec) , antiderivative size = 30, normalized size of antiderivative = 0.75 \[ \int \frac {(2+3 x)^4}{(1-2 x) (3+5 x)} \, dx=-\frac {27}{10} \, x^{3} - \frac {2079}{200} \, x^{2} - \frac {21951}{1000} \, x + \frac {1}{6875} \, \log \left (5 \, x + 3\right ) - \frac {2401}{176} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.06 (sec) , antiderivative size = 36, normalized size of antiderivative = 0.90 \[ \int \frac {(2+3 x)^4}{(1-2 x) (3+5 x)} \, dx=- \frac {27 x^{3}}{10} - \frac {2079 x^{2}}{200} - \frac {21951 x}{1000} - \frac {2401 \log {\left (x - \frac {1}{2} \right )}}{176} + \frac {\log {\left (x + \frac {3}{5} \right )}}{6875} \]
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Time = 0.21 (sec) , antiderivative size = 30, normalized size of antiderivative = 0.75 \[ \int \frac {(2+3 x)^4}{(1-2 x) (3+5 x)} \, dx=-\frac {27}{10} \, x^{3} - \frac {2079}{200} \, x^{2} - \frac {21951}{1000} \, x + \frac {1}{6875} \, \log \left (5 \, x + 3\right ) - \frac {2401}{176} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.27 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.80 \[ \int \frac {(2+3 x)^4}{(1-2 x) (3+5 x)} \, dx=-\frac {27}{10} \, x^{3} - \frac {2079}{200} \, x^{2} - \frac {21951}{1000} \, x + \frac {1}{6875} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {2401}{176} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
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Time = 0.04 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.65 \[ \int \frac {(2+3 x)^4}{(1-2 x) (3+5 x)} \, dx=\frac {\ln \left (x+\frac {3}{5}\right )}{6875}-\frac {2401\,\ln \left (x-\frac {1}{2}\right )}{176}-\frac {21951\,x}{1000}-\frac {2079\,x^2}{200}-\frac {27\,x^3}{10} \]
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