Integrand size = 20, antiderivative size = 30 \[ \int \frac {(2+3 x)^2 (3+5 x)}{1-2 x} \, dx=-\frac {443 x}{8}-\frac {219 x^2}{8}-\frac {15 x^3}{2}-\frac {539}{16} \log (1-2 x) \]
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Time = 0.01 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78} \[ \int \frac {(2+3 x)^2 (3+5 x)}{1-2 x} \, dx=-\frac {15 x^3}{2}-\frac {219 x^2}{8}-\frac {443 x}{8}-\frac {539}{16} \log (1-2 x) \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {443}{8}-\frac {219 x}{4}-\frac {45 x^2}{2}-\frac {539}{8 (-1+2 x)}\right ) \, dx \\ & = -\frac {443 x}{8}-\frac {219 x^2}{8}-\frac {15 x^3}{2}-\frac {539}{16} \log (1-2 x) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.90 \[ \int \frac {(2+3 x)^2 (3+5 x)}{1-2 x} \, dx=\frac {1}{32} \left (1135-1772 x-876 x^2-240 x^3-1078 \log (1-2 x)\right ) \]
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Time = 2.49 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.70
method | result | size |
parallelrisch | \(-\frac {15 x^{3}}{2}-\frac {219 x^{2}}{8}-\frac {443 x}{8}-\frac {539 \ln \left (x -\frac {1}{2}\right )}{16}\) | \(21\) |
default | \(-\frac {15 x^{3}}{2}-\frac {219 x^{2}}{8}-\frac {443 x}{8}-\frac {539 \ln \left (-1+2 x \right )}{16}\) | \(23\) |
norman | \(-\frac {15 x^{3}}{2}-\frac {219 x^{2}}{8}-\frac {443 x}{8}-\frac {539 \ln \left (-1+2 x \right )}{16}\) | \(23\) |
risch | \(-\frac {15 x^{3}}{2}-\frac {219 x^{2}}{8}-\frac {443 x}{8}-\frac {539 \ln \left (-1+2 x \right )}{16}\) | \(23\) |
meijerg | \(-\frac {539 \ln \left (1-2 x \right )}{16}-28 x -\frac {29 x \left (6 x +6\right )}{8}-\frac {15 x \left (16 x^{2}+12 x +12\right )}{32}\) | \(34\) |
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Time = 0.22 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.73 \[ \int \frac {(2+3 x)^2 (3+5 x)}{1-2 x} \, dx=-\frac {15}{2} \, x^{3} - \frac {219}{8} \, x^{2} - \frac {443}{8} \, x - \frac {539}{16} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.04 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.97 \[ \int \frac {(2+3 x)^2 (3+5 x)}{1-2 x} \, dx=- \frac {15 x^{3}}{2} - \frac {219 x^{2}}{8} - \frac {443 x}{8} - \frac {539 \log {\left (2 x - 1 \right )}}{16} \]
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Time = 0.21 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.73 \[ \int \frac {(2+3 x)^2 (3+5 x)}{1-2 x} \, dx=-\frac {15}{2} \, x^{3} - \frac {219}{8} \, x^{2} - \frac {443}{8} \, x - \frac {539}{16} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.28 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.77 \[ \int \frac {(2+3 x)^2 (3+5 x)}{1-2 x} \, dx=-\frac {15}{2} \, x^{3} - \frac {219}{8} \, x^{2} - \frac {443}{8} \, x - \frac {539}{16} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
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Time = 0.03 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.67 \[ \int \frac {(2+3 x)^2 (3+5 x)}{1-2 x} \, dx=-\frac {443\,x}{8}-\frac {539\,\ln \left (x-\frac {1}{2}\right )}{16}-\frac {219\,x^2}{8}-\frac {15\,x^3}{2} \]
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