Integrand size = 20, antiderivative size = 48 \[ \int \frac {(1-2 x) (2+3 x)^4}{(3+5 x)^2} \, dx=\frac {5511 x}{3125}+\frac {378 x^2}{625}-\frac {261 x^3}{125}-\frac {81 x^4}{50}-\frac {11}{15625 (3+5 x)}+\frac {26 \log (3+5 x)}{3125} \]
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Time = 0.02 (sec) , antiderivative size = 48, 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} \[ \int \frac {(1-2 x) (2+3 x)^4}{(3+5 x)^2} \, dx=-\frac {81 x^4}{50}-\frac {261 x^3}{125}+\frac {378 x^2}{625}+\frac {5511 x}{3125}-\frac {11}{15625 (5 x+3)}+\frac {26 \log (5 x+3)}{3125} \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {5511}{3125}+\frac {756 x}{625}-\frac {783 x^2}{125}-\frac {162 x^3}{25}+\frac {11}{3125 (3+5 x)^2}+\frac {26}{625 (3+5 x)}\right ) \, dx \\ & = \frac {5511 x}{3125}+\frac {378 x^2}{625}-\frac {261 x^3}{125}-\frac {81 x^4}{50}-\frac {11}{15625 (3+5 x)}+\frac {26 \log (3+5 x)}{3125} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.02 \[ \int \frac {(1-2 x) (2+3 x)^4}{(3+5 x)^2} \, dx=\frac {11233+51795 x+66450 x^2-20250 x^3-95625 x^4-50625 x^5+52 (3+5 x) \log (3+5 x)}{6250 (3+5 x)} \]
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Time = 2.20 (sec) , antiderivative size = 35, normalized size of antiderivative = 0.73
method | result | size |
risch | \(-\frac {81 x^{4}}{50}-\frac {261 x^{3}}{125}+\frac {378 x^{2}}{625}+\frac {5511 x}{3125}-\frac {11}{78125 \left (x +\frac {3}{5}\right )}+\frac {26 \ln \left (3+5 x \right )}{3125}\) | \(35\) |
default | \(\frac {5511 x}{3125}+\frac {378 x^{2}}{625}-\frac {261 x^{3}}{125}-\frac {81 x^{4}}{50}-\frac {11}{15625 \left (3+5 x \right )}+\frac {26 \ln \left (3+5 x \right )}{3125}\) | \(37\) |
norman | \(\frac {\frac {9922}{1875} x +\frac {1329}{125} x^{2}-\frac {81}{25} x^{3}-\frac {153}{10} x^{4}-\frac {81}{10} x^{5}}{3+5 x}+\frac {26 \ln \left (3+5 x \right )}{3125}\) | \(42\) |
parallelrisch | \(\frac {-151875 x^{5}-286875 x^{4}-60750 x^{3}+780 \ln \left (x +\frac {3}{5}\right ) x +199350 x^{2}+468 \ln \left (x +\frac {3}{5}\right )+99220 x}{56250+93750 x}\) | \(47\) |
meijerg | \(-\frac {112 x}{45 \left (1+\frac {5 x}{3}\right )}+\frac {26 \ln \left (1+\frac {5 x}{3}\right )}{3125}+\frac {8 x \left (5 x +6\right )}{25 \left (1+\frac {5 x}{3}\right )}+\frac {162 x \left (-\frac {50}{9} x^{2}+10 x +12\right )}{125 \left (1+\frac {5 x}{3}\right )}-\frac {1053 x \left (\frac {625}{27} x^{3}-\frac {250}{9} x^{2}+50 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )}+\frac {729 x \left (-\frac {625}{27} x^{4}+\frac {625}{27} x^{3}-\frac {250}{9} x^{2}+50 x +60\right )}{6250 \left (1+\frac {5 x}{3}\right )}\) | \(110\) |
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Time = 0.22 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.98 \[ \int \frac {(1-2 x) (2+3 x)^4}{(3+5 x)^2} \, dx=-\frac {253125 \, x^{5} + 478125 \, x^{4} + 101250 \, x^{3} - 332250 \, x^{2} - 260 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 165330 \, x + 22}{31250 \, {\left (5 \, x + 3\right )}} \]
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Time = 0.05 (sec) , antiderivative size = 41, normalized size of antiderivative = 0.85 \[ \int \frac {(1-2 x) (2+3 x)^4}{(3+5 x)^2} \, dx=- \frac {81 x^{4}}{50} - \frac {261 x^{3}}{125} + \frac {378 x^{2}}{625} + \frac {5511 x}{3125} + \frac {26 \log {\left (5 x + 3 \right )}}{3125} - \frac {11}{78125 x + 46875} \]
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Time = 0.20 (sec) , antiderivative size = 36, normalized size of antiderivative = 0.75 \[ \int \frac {(1-2 x) (2+3 x)^4}{(3+5 x)^2} \, dx=-\frac {81}{50} \, x^{4} - \frac {261}{125} \, x^{3} + \frac {378}{625} \, x^{2} + \frac {5511}{3125} \, x - \frac {11}{15625 \, {\left (5 \, x + 3\right )}} + \frac {26}{3125} \, \log \left (5 \, x + 3\right ) \]
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Time = 0.27 (sec) , antiderivative size = 66, normalized size of antiderivative = 1.38 \[ \int \frac {(1-2 x) (2+3 x)^4}{(3+5 x)^2} \, dx=\frac {3}{31250} \, {\left (5 \, x + 3\right )}^{4} {\left (\frac {150}{5 \, x + 3} + \frac {360}{{\left (5 \, x + 3\right )}^{2}} + \frac {380}{{\left (5 \, x + 3\right )}^{3}} - 27\right )} - \frac {11}{15625 \, {\left (5 \, x + 3\right )}} - \frac {26}{3125} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) \]
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Time = 0.03 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x) (2+3 x)^4}{(3+5 x)^2} \, dx=\frac {5511\,x}{3125}+\frac {26\,\ln \left (x+\frac {3}{5}\right )}{3125}-\frac {11}{78125\,\left (x+\frac {3}{5}\right )}+\frac {378\,x^2}{625}-\frac {261\,x^3}{125}-\frac {81\,x^4}{50} \]
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