Optimal. Leaf size=69 \[ -\frac{1944 x^7}{175}-\frac{1026 x^6}{125}+\frac{44982 x^5}{3125}+\frac{108387 x^4}{12500}-\frac{26594 x^3}{3125}-\frac{507023 x^2}{156250}+\frac{1382328 x}{390625}-\frac{1331}{1953125 (5 x+3)}+\frac{19239 \log (5 x+3)}{1953125} \]
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Rubi [A] time = 0.0349932, antiderivative size = 69, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {88} \[ -\frac{1944 x^7}{175}-\frac{1026 x^6}{125}+\frac{44982 x^5}{3125}+\frac{108387 x^4}{12500}-\frac{26594 x^3}{3125}-\frac{507023 x^2}{156250}+\frac{1382328 x}{390625}-\frac{1331}{1953125 (5 x+3)}+\frac{19239 \log (5 x+3)}{1953125} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3 (2+3 x)^5}{(3+5 x)^2} \, dx &=\int \left (\frac{1382328}{390625}-\frac{507023 x}{78125}-\frac{79782 x^2}{3125}+\frac{108387 x^3}{3125}+\frac{44982 x^4}{625}-\frac{6156 x^5}{125}-\frac{1944 x^6}{25}+\frac{1331}{390625 (3+5 x)^2}+\frac{19239}{390625 (3+5 x)}\right ) \, dx\\ &=\frac{1382328 x}{390625}-\frac{507023 x^2}{156250}-\frac{26594 x^3}{3125}+\frac{108387 x^4}{12500}+\frac{44982 x^5}{3125}-\frac{1026 x^6}{125}-\frac{1944 x^7}{175}-\frac{1331}{1953125 (3+5 x)}+\frac{19239 \log (3+5 x)}{1953125}\\ \end{align*}
Mathematica [A] time = 0.0326393, size = 66, normalized size = 0.96 \[ \frac{-15187500000 x^8-20334375000 x^7+12946500000 x^6+23662603125 x^5-4521978125 x^4-11417376250 x^3+2176277250 x^2+4982083965 x+2693460 (5 x+3) \log (6 (5 x+3))+1247330759}{273437500 (5 x+3)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 52, normalized size = 0.8 \begin{align*}{\frac{1382328\,x}{390625}}-{\frac{507023\,{x}^{2}}{156250}}-{\frac{26594\,{x}^{3}}{3125}}+{\frac{108387\,{x}^{4}}{12500}}+{\frac{44982\,{x}^{5}}{3125}}-{\frac{1026\,{x}^{6}}{125}}-{\frac{1944\,{x}^{7}}{175}}-{\frac{1331}{5859375+9765625\,x}}+{\frac{19239\,\ln \left ( 3+5\,x \right ) }{1953125}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02115, size = 69, normalized size = 1. \begin{align*} -\frac{1944}{175} \, x^{7} - \frac{1026}{125} \, x^{6} + \frac{44982}{3125} \, x^{5} + \frac{108387}{12500} \, x^{4} - \frac{26594}{3125} \, x^{3} - \frac{507023}{156250} \, x^{2} + \frac{1382328}{390625} \, x - \frac{1331}{1953125 \,{\left (5 \, x + 3\right )}} + \frac{19239}{1953125} \, \log \left (5 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.22311, size = 262, normalized size = 3.8 \begin{align*} -\frac{3037500000 \, x^{8} + 4066875000 \, x^{7} - 2589300000 \, x^{6} - 4732520625 \, x^{5} + 904395625 \, x^{4} + 2283475250 \, x^{3} - 435255450 \, x^{2} - 538692 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 580577760 \, x + 37268}{54687500 \,{\left (5 \, x + 3\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.111758, size = 61, normalized size = 0.88 \begin{align*} - \frac{1944 x^{7}}{175} - \frac{1026 x^{6}}{125} + \frac{44982 x^{5}}{3125} + \frac{108387 x^{4}}{12500} - \frac{26594 x^{3}}{3125} - \frac{507023 x^{2}}{156250} + \frac{1382328 x}{390625} + \frac{19239 \log{\left (5 x + 3 \right )}}{1953125} - \frac{1331}{9765625 x + 5859375} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.99473, size = 126, normalized size = 1.83 \begin{align*} \frac{1}{273437500} \,{\left (5 \, x + 3\right )}^{7}{\left (\frac{672840}{5 \, x + 3} - \frac{3503304}{{\left (5 \, x + 3\right )}^{2}} + \frac{2251305}{{\left (5 \, x + 3\right )}^{3}} + \frac{16557100}{{\left (5 \, x + 3\right )}^{4}} + \frac{20720140}{{\left (5 \, x + 3\right )}^{5}} + \frac{15264480}{{\left (5 \, x + 3\right )}^{6}} - 38880\right )} - \frac{1331}{1953125 \,{\left (5 \, x + 3\right )}} - \frac{19239}{1953125} \, \log \left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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