Optimal. Leaf size=69 \[ \frac{18225 x^7}{28}+\frac{37665 x^6}{8}+\frac{1295919 x^5}{80}+\frac{575775 x^4}{16}+\frac{3851307 x^3}{64}+\frac{11140101 x^2}{128}+\frac{35458963 x}{256}+\frac{14235529}{512 (1-2 x)}+\frac{12386759}{128} \log (1-2 x) \]
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Rubi [A] time = 0.0376166, 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} \[ \frac{18225 x^7}{28}+\frac{37665 x^6}{8}+\frac{1295919 x^5}{80}+\frac{575775 x^4}{16}+\frac{3851307 x^3}{64}+\frac{11140101 x^2}{128}+\frac{35458963 x}{256}+\frac{14235529}{512 (1-2 x)}+\frac{12386759}{128} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^6 (3+5 x)^2}{(1-2 x)^2} \, dx &=\int \left (\frac{35458963}{256}+\frac{11140101 x}{64}+\frac{11553921 x^2}{64}+\frac{575775 x^3}{4}+\frac{1295919 x^4}{16}+\frac{112995 x^5}{4}+\frac{18225 x^6}{4}+\frac{14235529}{256 (-1+2 x)^2}+\frac{12386759}{64 (-1+2 x)}\right ) \, dx\\ &=\frac{14235529}{512 (1-2 x)}+\frac{35458963 x}{256}+\frac{11140101 x^2}{128}+\frac{3851307 x^3}{64}+\frac{575775 x^4}{16}+\frac{1295919 x^5}{80}+\frac{37665 x^6}{8}+\frac{18225 x^7}{28}+\frac{12386759}{128} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0206732, size = 64, normalized size = 0.93 \[ \frac{23328000 x^8+157075200 x^7+496202112 x^6+999450144 x^5+1511863920 x^4+2040862320 x^3+3404640680 x^2-6115223546 x+1734146260 (2 x-1) \log (1-2 x)+1318304553}{17920 (2 x-1)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 52, normalized size = 0.8 \begin{align*}{\frac{18225\,{x}^{7}}{28}}+{\frac{37665\,{x}^{6}}{8}}+{\frac{1295919\,{x}^{5}}{80}}+{\frac{575775\,{x}^{4}}{16}}+{\frac{3851307\,{x}^{3}}{64}}+{\frac{11140101\,{x}^{2}}{128}}+{\frac{35458963\,x}{256}}+{\frac{12386759\,\ln \left ( 2\,x-1 \right ) }{128}}-{\frac{14235529}{1024\,x-512}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.08793, size = 69, normalized size = 1. \begin{align*} \frac{18225}{28} \, x^{7} + \frac{37665}{8} \, x^{6} + \frac{1295919}{80} \, x^{5} + \frac{575775}{16} \, x^{4} + \frac{3851307}{64} \, x^{3} + \frac{11140101}{128} \, x^{2} + \frac{35458963}{256} \, x - \frac{14235529}{512 \,{\left (2 \, x - 1\right )}} + \frac{12386759}{128} \, \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 = 1.28208, size = 265, normalized size = 3.84 \begin{align*} \frac{23328000 \, x^{8} + 157075200 \, x^{7} + 496202112 \, x^{6} + 999450144 \, x^{5} + 1511863920 \, x^{4} + 2040862320 \, x^{3} + 3404640680 \, x^{2} + 1734146260 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 2482127410 \, x - 498243515}{17920 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.112597, size = 61, normalized size = 0.88 \begin{align*} \frac{18225 x^{7}}{28} + \frac{37665 x^{6}}{8} + \frac{1295919 x^{5}}{80} + \frac{575775 x^{4}}{16} + \frac{3851307 x^{3}}{64} + \frac{11140101 x^{2}}{128} + \frac{35458963 x}{256} + \frac{12386759 \log{\left (2 x - 1 \right )}}{128} - \frac{14235529}{1024 x - 512} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.06777, size = 126, normalized size = 1.83 \begin{align*} \frac{1}{17920} \,{\left (2 \, x - 1\right )}^{7}{\left (\frac{1956150}{2 \, x - 1} + \frac{18894708}{{\left (2 \, x - 1\right )}^{2}} + \frac{108624915}{{\left (2 \, x - 1\right )}^{3}} + \frac{416281950}{{\left (2 \, x - 1\right )}^{4}} + \frac{1148518350}{{\left (2 \, x - 1\right )}^{5}} + \frac{2640379700}{{\left (2 \, x - 1\right )}^{6}} + 91125\right )} - \frac{14235529}{512 \,{\left (2 \, x - 1\right )}} - \frac{12386759}{128} \, \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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