Integrand size = 20, antiderivative size = 52 \[ \int \frac {(1-2 x) (2+3 x)^4}{(3+5 x)^3} \, dx=\frac {1647 x}{3125}-\frac {297 x^2}{1250}-\frac {54 x^3}{125}-\frac {11}{31250 (3+5 x)^2}-\frac {26}{3125 (3+5 x)}+\frac {114 \log (3+5 x)}{3125} \]
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Time = 0.02 (sec) , antiderivative size = 52, 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} \[ \int \frac {(1-2 x) (2+3 x)^4}{(3+5 x)^3} \, dx=-\frac {54 x^3}{125}-\frac {297 x^2}{1250}+\frac {1647 x}{3125}-\frac {26}{3125 (5 x+3)}-\frac {11}{31250 (5 x+3)^2}+\frac {114 \log (5 x+3)}{3125} \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {1647}{3125}-\frac {297 x}{625}-\frac {162 x^2}{125}+\frac {11}{3125 (3+5 x)^3}+\frac {26}{625 (3+5 x)^2}+\frac {114}{625 (3+5 x)}\right ) \, dx \\ & = \frac {1647 x}{3125}-\frac {297 x^2}{1250}-\frac {54 x^3}{125}-\frac {11}{31250 (3+5 x)^2}-\frac {26}{3125 (3+5 x)}+\frac {114 \log (3+5 x)}{3125} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 51, normalized size of antiderivative = 0.98 \[ \int \frac {(1-2 x) (2+3 x)^4}{(3+5 x)^3} \, dx=\frac {17192+87220 x+133650 x^2+13500 x^3-118125 x^4-67500 x^5+228 (3+5 x)^2 \log (3+5 x)}{6250 (3+5 x)^2} \]
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Time = 2.96 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.71
method | result | size |
risch | \(-\frac {54 x^{3}}{125}-\frac {297 x^{2}}{1250}+\frac {1647 x}{3125}+\frac {-\frac {26 x}{625}-\frac {791}{31250}}{\left (3+5 x \right )^{2}}+\frac {114 \ln \left (3+5 x \right )}{3125}\) | \(37\) |
default | \(\frac {1647 x}{3125}-\frac {297 x^{2}}{1250}-\frac {54 x^{3}}{125}-\frac {11}{31250 \left (3+5 x \right )^{2}}-\frac {26}{3125 \left (3+5 x \right )}+\frac {114 \ln \left (3+5 x \right )}{3125}\) | \(41\) |
norman | \(\frac {\frac {8974}{1875} x +\frac {15461}{1125} x^{2}+\frac {54}{25} x^{3}-\frac {189}{10} x^{4}-\frac {54}{5} x^{5}}{\left (3+5 x \right )^{2}}+\frac {114 \ln \left (3+5 x \right )}{3125}\) | \(42\) |
parallelrisch | \(\frac {-607500 x^{5}-1063125 x^{4}+51300 \ln \left (x +\frac {3}{5}\right ) x^{2}+121500 x^{3}+61560 \ln \left (x +\frac {3}{5}\right ) x +773050 x^{2}+18468 \ln \left (x +\frac {3}{5}\right )+269220 x}{56250 \left (3+5 x \right )^{2}}\) | \(56\) |
meijerg | \(\frac {8 x \left (\frac {5 x}{3}+2\right )}{27 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {32 x^{2}}{27 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {4 x \left (15 x +6\right )}{75 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {114 \ln \left (1+\frac {5 x}{3}\right )}{3125}-\frac {54 x \left (\frac {100}{9} x^{2}+30 x +12\right )}{125 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {1053 x \left (-\frac {625}{27} x^{3}+\frac {500}{9} x^{2}+150 x +60\right )}{6250 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {243 x \left (\frac {1250}{81} x^{4}-\frac {625}{27} x^{3}+\frac {500}{9} x^{2}+150 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )^{2}}\) | \(127\) |
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Time = 0.22 (sec) , antiderivative size = 57, normalized size of antiderivative = 1.10 \[ \int \frac {(1-2 x) (2+3 x)^4}{(3+5 x)^3} \, dx=-\frac {337500 \, x^{5} + 590625 \, x^{4} - 67500 \, x^{3} - 427275 \, x^{2} - 1140 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 146930 \, x + 791}{31250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
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Time = 0.05 (sec) , antiderivative size = 42, normalized size of antiderivative = 0.81 \[ \int \frac {(1-2 x) (2+3 x)^4}{(3+5 x)^3} \, dx=- \frac {54 x^{3}}{125} - \frac {297 x^{2}}{1250} + \frac {1647 x}{3125} - \frac {1300 x + 791}{781250 x^{2} + 937500 x + 281250} + \frac {114 \log {\left (5 x + 3 \right )}}{3125} \]
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Time = 0.20 (sec) , antiderivative size = 41, normalized size of antiderivative = 0.79 \[ \int \frac {(1-2 x) (2+3 x)^4}{(3+5 x)^3} \, dx=-\frac {54}{125} \, x^{3} - \frac {297}{1250} \, x^{2} + \frac {1647}{3125} \, x - \frac {1300 \, x + 791}{31250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {114}{3125} \, \log \left (5 \, x + 3\right ) \]
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Time = 0.27 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x) (2+3 x)^4}{(3+5 x)^3} \, dx=-\frac {54}{125} \, x^{3} - \frac {297}{1250} \, x^{2} + \frac {1647}{3125} \, x - \frac {1300 \, x + 791}{31250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {114}{3125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
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Time = 0.03 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x) (2+3 x)^4}{(3+5 x)^3} \, dx=\frac {1647\,x}{3125}+\frac {114\,\ln \left (x+\frac {3}{5}\right )}{3125}-\frac {\frac {26\,x}{15625}+\frac {791}{781250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}}-\frac {297\,x^2}{1250}-\frac {54\,x^3}{125} \]
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