Integrand size = 22, antiderivative size = 51 \[ \int \frac {(1-2 x)^2 (2+3 x)^4}{3+5 x} \, dx=\frac {83293 x}{15625}+\frac {5569 x^2}{6250}-\frac {7841 x^3}{625}-\frac {3159 x^4}{500}+\frac {1728 x^5}{125}+\frac {54 x^6}{5}+\frac {121 \log (3+5 x)}{78125} \]
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Time = 0.02 (sec) , antiderivative size = 51, 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} \[ \int \frac {(1-2 x)^2 (2+3 x)^4}{3+5 x} \, dx=\frac {54 x^6}{5}+\frac {1728 x^5}{125}-\frac {3159 x^4}{500}-\frac {7841 x^3}{625}+\frac {5569 x^2}{6250}+\frac {83293 x}{15625}+\frac {121 \log (5 x+3)}{78125} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {83293}{15625}+\frac {5569 x}{3125}-\frac {23523 x^2}{625}-\frac {3159 x^3}{125}+\frac {1728 x^4}{25}+\frac {324 x^5}{5}+\frac {121}{15625 (3+5 x)}\right ) \, dx \\ & = \frac {83293 x}{15625}+\frac {5569 x^2}{6250}-\frac {7841 x^3}{625}-\frac {3159 x^4}{500}+\frac {1728 x^5}{125}+\frac {54 x^6}{5}+\frac {121 \log (3+5 x)}{78125} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 42, normalized size of antiderivative = 0.82 \[ \int \frac {(1-2 x)^2 (2+3 x)^4}{3+5 x} \, dx=\frac {2433921+8329300 x+1392250 x^2-19602500 x^3-9871875 x^4+21600000 x^5+16875000 x^6+2420 \log (3+5 x)}{1562500} \]
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Time = 2.33 (sec) , antiderivative size = 36, normalized size of antiderivative = 0.71
method | result | size |
parallelrisch | \(\frac {54 x^{6}}{5}+\frac {1728 x^{5}}{125}-\frac {3159 x^{4}}{500}-\frac {7841 x^{3}}{625}+\frac {5569 x^{2}}{6250}+\frac {83293 x}{15625}+\frac {121 \ln \left (x +\frac {3}{5}\right )}{78125}\) | \(36\) |
default | \(\frac {83293 x}{15625}+\frac {5569 x^{2}}{6250}-\frac {7841 x^{3}}{625}-\frac {3159 x^{4}}{500}+\frac {1728 x^{5}}{125}+\frac {54 x^{6}}{5}+\frac {121 \ln \left (3+5 x \right )}{78125}\) | \(38\) |
norman | \(\frac {83293 x}{15625}+\frac {5569 x^{2}}{6250}-\frac {7841 x^{3}}{625}-\frac {3159 x^{4}}{500}+\frac {1728 x^{5}}{125}+\frac {54 x^{6}}{5}+\frac {121 \ln \left (3+5 x \right )}{78125}\) | \(38\) |
risch | \(\frac {83293 x}{15625}+\frac {5569 x^{2}}{6250}-\frac {7841 x^{3}}{625}-\frac {3159 x^{4}}{500}+\frac {1728 x^{5}}{125}+\frac {54 x^{6}}{5}+\frac {121 \ln \left (3+5 x \right )}{78125}\) | \(38\) |
meijerg | \(\frac {121 \ln \left (1+\frac {5 x}{3}\right )}{78125}+\frac {32 x}{5}+\frac {52 x \left (-5 x +6\right )}{25}-\frac {198 x \left (\frac {100}{9} x^{2}-10 x +12\right )}{125}-\frac {729 x \left (-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{12500}+\frac {729 x \left (\frac {2500}{27} x^{4}-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{3125}-\frac {6561 x \left (-\frac {218750}{243} x^{5}+\frac {17500}{27} x^{4}-\frac {4375}{9} x^{3}+\frac {3500}{9} x^{2}-350 x +420\right )}{546875}\) | \(103\) |
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Time = 0.22 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.73 \[ \int \frac {(1-2 x)^2 (2+3 x)^4}{3+5 x} \, dx=\frac {54}{5} \, x^{6} + \frac {1728}{125} \, x^{5} - \frac {3159}{500} \, x^{4} - \frac {7841}{625} \, x^{3} + \frac {5569}{6250} \, x^{2} + \frac {83293}{15625} \, x + \frac {121}{78125} \, \log \left (5 \, x + 3\right ) \]
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Time = 0.04 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.94 \[ \int \frac {(1-2 x)^2 (2+3 x)^4}{3+5 x} \, dx=\frac {54 x^{6}}{5} + \frac {1728 x^{5}}{125} - \frac {3159 x^{4}}{500} - \frac {7841 x^{3}}{625} + \frac {5569 x^{2}}{6250} + \frac {83293 x}{15625} + \frac {121 \log {\left (5 x + 3 \right )}}{78125} \]
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Time = 0.20 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.73 \[ \int \frac {(1-2 x)^2 (2+3 x)^4}{3+5 x} \, dx=\frac {54}{5} \, x^{6} + \frac {1728}{125} \, x^{5} - \frac {3159}{500} \, x^{4} - \frac {7841}{625} \, x^{3} + \frac {5569}{6250} \, x^{2} + \frac {83293}{15625} \, x + \frac {121}{78125} \, \log \left (5 \, x + 3\right ) \]
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Time = 0.27 (sec) , antiderivative size = 38, normalized size of antiderivative = 0.75 \[ \int \frac {(1-2 x)^2 (2+3 x)^4}{3+5 x} \, dx=\frac {54}{5} \, x^{6} + \frac {1728}{125} \, x^{5} - \frac {3159}{500} \, x^{4} - \frac {7841}{625} \, x^{3} + \frac {5569}{6250} \, x^{2} + \frac {83293}{15625} \, x + \frac {121}{78125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
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Time = 0.05 (sec) , antiderivative size = 35, normalized size of antiderivative = 0.69 \[ \int \frac {(1-2 x)^2 (2+3 x)^4}{3+5 x} \, dx=\frac {83293\,x}{15625}+\frac {121\,\ln \left (x+\frac {3}{5}\right )}{78125}+\frac {5569\,x^2}{6250}-\frac {7841\,x^3}{625}-\frac {3159\,x^4}{500}+\frac {1728\,x^5}{125}+\frac {54\,x^6}{5} \]
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