Integrand size = 22, antiderivative size = 47 \[ \int \frac {(2+3 x)^5}{(1-2 x) (3+5 x)} \, dx=-\frac {848277 x}{10000}-\frac {107433 x^2}{2000}-\frac {2619 x^3}{100}-\frac {243 x^4}{40}-\frac {16807}{352} \log (1-2 x)+\frac {\log (3+5 x)}{34375} \]
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Time = 0.01 (sec) , antiderivative size = 47, 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} \[ \int \frac {(2+3 x)^5}{(1-2 x) (3+5 x)} \, dx=-\frac {243 x^4}{40}-\frac {2619 x^3}{100}-\frac {107433 x^2}{2000}-\frac {848277 x}{10000}-\frac {16807}{352} \log (1-2 x)+\frac {\log (5 x+3)}{34375} \]
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Rule 84
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {848277}{10000}-\frac {107433 x}{1000}-\frac {7857 x^2}{100}-\frac {243 x^3}{10}-\frac {16807}{176 (-1+2 x)}+\frac {1}{6875 (3+5 x)}\right ) \, dx \\ & = -\frac {848277 x}{10000}-\frac {107433 x^2}{2000}-\frac {2619 x^3}{100}-\frac {243 x^4}{40}-\frac {16807}{352} \log (1-2 x)+\frac {\log (3+5 x)}{34375} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 45, normalized size of antiderivative = 0.96 \[ \int \frac {(2+3 x)^5}{(1-2 x) (3+5 x)} \, dx=\frac {-110 \left (392378+848277 x+537165 x^2+261900 x^3+60750 x^4\right )-52521875 \log (3-6 x)+32 \log (-3 (3+5 x))}{1100000} \]
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Time = 2.55 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.68
method | result | size |
parallelrisch | \(-\frac {243 x^{4}}{40}-\frac {2619 x^{3}}{100}-\frac {107433 x^{2}}{2000}-\frac {848277 x}{10000}+\frac {\ln \left (x +\frac {3}{5}\right )}{34375}-\frac {16807 \ln \left (x -\frac {1}{2}\right )}{352}\) | \(32\) |
default | \(-\frac {243 x^{4}}{40}-\frac {2619 x^{3}}{100}-\frac {107433 x^{2}}{2000}-\frac {848277 x}{10000}+\frac {\ln \left (3+5 x \right )}{34375}-\frac {16807 \ln \left (-1+2 x \right )}{352}\) | \(36\) |
norman | \(-\frac {243 x^{4}}{40}-\frac {2619 x^{3}}{100}-\frac {107433 x^{2}}{2000}-\frac {848277 x}{10000}+\frac {\ln \left (3+5 x \right )}{34375}-\frac {16807 \ln \left (-1+2 x \right )}{352}\) | \(36\) |
risch | \(-\frac {243 x^{4}}{40}-\frac {2619 x^{3}}{100}-\frac {107433 x^{2}}{2000}-\frac {848277 x}{10000}+\frac {\ln \left (3+5 x \right )}{34375}-\frac {16807 \ln \left (-1+2 x \right )}{352}\) | \(36\) |
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none
Time = 0.23 (sec) , antiderivative size = 35, normalized size of antiderivative = 0.74 \[ \int \frac {(2+3 x)^5}{(1-2 x) (3+5 x)} \, dx=-\frac {243}{40} \, x^{4} - \frac {2619}{100} \, x^{3} - \frac {107433}{2000} \, x^{2} - \frac {848277}{10000} \, x + \frac {1}{34375} \, \log \left (5 \, x + 3\right ) - \frac {16807}{352} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.07 (sec) , antiderivative size = 42, normalized size of antiderivative = 0.89 \[ \int \frac {(2+3 x)^5}{(1-2 x) (3+5 x)} \, dx=- \frac {243 x^{4}}{40} - \frac {2619 x^{3}}{100} - \frac {107433 x^{2}}{2000} - \frac {848277 x}{10000} - \frac {16807 \log {\left (x - \frac {1}{2} \right )}}{352} + \frac {\log {\left (x + \frac {3}{5} \right )}}{34375} \]
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none
Time = 0.20 (sec) , antiderivative size = 35, normalized size of antiderivative = 0.74 \[ \int \frac {(2+3 x)^5}{(1-2 x) (3+5 x)} \, dx=-\frac {243}{40} \, x^{4} - \frac {2619}{100} \, x^{3} - \frac {107433}{2000} \, x^{2} - \frac {848277}{10000} \, x + \frac {1}{34375} \, \log \left (5 \, x + 3\right ) - \frac {16807}{352} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.27 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.79 \[ \int \frac {(2+3 x)^5}{(1-2 x) (3+5 x)} \, dx=-\frac {243}{40} \, x^{4} - \frac {2619}{100} \, x^{3} - \frac {107433}{2000} \, x^{2} - \frac {848277}{10000} \, x + \frac {1}{34375} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {16807}{352} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
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Time = 1.54 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.66 \[ \int \frac {(2+3 x)^5}{(1-2 x) (3+5 x)} \, dx=\frac {\ln \left (x+\frac {3}{5}\right )}{34375}-\frac {16807\,\ln \left (x-\frac {1}{2}\right )}{352}-\frac {848277\,x}{10000}-\frac {107433\,x^2}{2000}-\frac {2619\,x^3}{100}-\frac {243\,x^4}{40} \]
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