Optimal. Leaf size=76 \[ \frac{54675 x^8}{32}+\frac{375435 x^7}{28}+\frac{1597239 x^6}{32}+\frac{4750569 x^5}{40}+\frac{53086563 x^4}{256}+\frac{18842715 x^3}{64}+\frac{195497697 x^2}{512}+\frac{9077405 x}{16}+\frac{99648703}{1024 (1-2 x)}+\frac{389535839 \log (1-2 x)}{1024} \]
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Rubi [A] time = 0.0433517, antiderivative size = 76, 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} \[ \frac{54675 x^8}{32}+\frac{375435 x^7}{28}+\frac{1597239 x^6}{32}+\frac{4750569 x^5}{40}+\frac{53086563 x^4}{256}+\frac{18842715 x^3}{64}+\frac{195497697 x^2}{512}+\frac{9077405 x}{16}+\frac{99648703}{1024 (1-2 x)}+\frac{389535839 \log (1-2 x)}{1024} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^7 (3+5 x)^2}{(1-2 x)^2} \, dx &=\int \left (\frac{9077405}{16}+\frac{195497697 x}{256}+\frac{56528145 x^2}{64}+\frac{53086563 x^3}{64}+\frac{4750569 x^4}{8}+\frac{4791717 x^5}{16}+\frac{375435 x^6}{4}+\frac{54675 x^7}{4}+\frac{99648703}{512 (-1+2 x)^2}+\frac{389535839}{512 (-1+2 x)}\right ) \, dx\\ &=\frac{99648703}{1024 (1-2 x)}+\frac{9077405 x}{16}+\frac{195497697 x^2}{512}+\frac{18842715 x^3}{64}+\frac{53086563 x^4}{256}+\frac{4750569 x^5}{40}+\frac{1597239 x^6}{32}+\frac{375435 x^7}{28}+\frac{54675 x^8}{32}+\frac{389535839 \log (1-2 x)}{1024}\\ \end{align*}
Mathematica [A] time = 0.0168576, size = 69, normalized size = 0.91 \[ \frac{979776000 x^9+7199020800 x^8+24778068480 x^7+53792895744 x^6+84861822528 x^5+109373775840 x^4+134542057440 x^3+215855484880 x^2-411248888662 x+109070034920 (2 x-1) \log (1-2 x)+96389258691}{286720 (2 x-1)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 57, normalized size = 0.8 \begin{align*}{\frac{54675\,{x}^{8}}{32}}+{\frac{375435\,{x}^{7}}{28}}+{\frac{1597239\,{x}^{6}}{32}}+{\frac{4750569\,{x}^{5}}{40}}+{\frac{53086563\,{x}^{4}}{256}}+{\frac{18842715\,{x}^{3}}{64}}+{\frac{195497697\,{x}^{2}}{512}}+{\frac{9077405\,x}{16}}+{\frac{389535839\,\ln \left ( 2\,x-1 \right ) }{1024}}-{\frac{99648703}{2048\,x-1024}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.75828, size = 76, normalized size = 1. \begin{align*} \frac{54675}{32} \, x^{8} + \frac{375435}{28} \, x^{7} + \frac{1597239}{32} \, x^{6} + \frac{4750569}{40} \, x^{5} + \frac{53086563}{256} \, x^{4} + \frac{18842715}{64} \, x^{3} + \frac{195497697}{512} \, x^{2} + \frac{9077405}{16} \, x - \frac{99648703}{1024 \,{\left (2 \, x - 1\right )}} + \frac{389535839}{1024} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.35257, size = 301, normalized size = 3.96 \begin{align*} \frac{122472000 \, x^{9} + 899877600 \, x^{8} + 3097258560 \, x^{7} + 6724111968 \, x^{6} + 10607727816 \, x^{5} + 13671721980 \, x^{4} + 16817757180 \, x^{3} + 26981935610 \, x^{2} + 13633754365 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 20333387200 \, x - 3487704605}{35840 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.118876, size = 68, normalized size = 0.89 \begin{align*} \frac{54675 x^{8}}{32} + \frac{375435 x^{7}}{28} + \frac{1597239 x^{6}}{32} + \frac{4750569 x^{5}}{40} + \frac{53086563 x^{4}}{256} + \frac{18842715 x^{3}}{64} + \frac{195497697 x^{2}}{512} + \frac{9077405 x}{16} + \frac{389535839 \log{\left (2 x - 1 \right )}}{1024} - \frac{99648703}{2048 x - 1024} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.15119, size = 138, normalized size = 1.82 \begin{align*} \frac{1}{286720} \,{\left (2 \, x - 1\right )}^{8}{\left (\frac{45343800}{2 \, x - 1} + \frac{487438560}{{\left (2 \, x - 1\right )}^{2}} + \frac{3143702016}{{\left (2 \, x - 1\right )}^{3}} + \frac{13576070340}{{\left (2 \, x - 1\right )}^{4}} + \frac{41688082800}{{\left (2 \, x - 1\right )}^{5}} + \frac{96001584000}{{\left (2 \, x - 1\right )}^{6}} + \frac{189480773440}{{\left (2 \, x - 1\right )}^{7}} + 1913625\right )} - \frac{99648703}{1024 \,{\left (2 \, x - 1\right )}} - \frac{389535839}{1024} \, \log \left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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