Optimal. Leaf size=83 \[ \frac{30375 x^9}{4}+\frac{127575 x^8}{2}+\frac{28463805 x^7}{112}+\frac{20626947 x^6}{32}+\frac{379446471 x^5}{320}+\frac{220950207 x^4}{128}+\frac{551942075 x^3}{256}+\frac{1312685491 x^2}{512}+\frac{3690540955 x}{1024}+\frac{1096135733}{2048 (1-2 x)}+\frac{298946109}{128} \log (1-2 x) \]
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Rubi [A] time = 0.046967, antiderivative size = 83, 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} \[ \frac{30375 x^9}{4}+\frac{127575 x^8}{2}+\frac{28463805 x^7}{112}+\frac{20626947 x^6}{32}+\frac{379446471 x^5}{320}+\frac{220950207 x^4}{128}+\frac{551942075 x^3}{256}+\frac{1312685491 x^2}{512}+\frac{3690540955 x}{1024}+\frac{1096135733}{2048 (1-2 x)}+\frac{298946109}{128} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^7 (3+5 x)^3}{(1-2 x)^2} \, dx &=\int \left (\frac{3690540955}{1024}+\frac{1312685491 x}{256}+\frac{1655826225 x^2}{256}+\frac{220950207 x^3}{32}+\frac{379446471 x^4}{64}+\frac{61880841 x^5}{16}+\frac{28463805 x^6}{16}+510300 x^7+\frac{273375 x^8}{4}+\frac{1096135733}{1024 (-1+2 x)^2}+\frac{298946109}{64 (-1+2 x)}\right ) \, dx\\ &=\frac{1096135733}{2048 (1-2 x)}+\frac{3690540955 x}{1024}+\frac{1312685491 x^2}{512}+\frac{551942075 x^3}{256}+\frac{220950207 x^4}{128}+\frac{379446471 x^5}{320}+\frac{20626947 x^6}{32}+\frac{28463805 x^7}{112}+\frac{127575 x^8}{2}+\frac{30375 x^9}{4}+\frac{298946109}{128} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0186524, size = 74, normalized size = 0.89 \[ \frac{1088640000 x^{10}+8600256000 x^9+31861382400 x^8+74191887360 x^7+123787657728 x^6+162468222336 x^5+185355446080 x^4+213008156480 x^3+332899764960 x^2-669744799994 x+167409821040 (2 x-1) \log (1-2 x)+167338715917}{71680 (2 x-1)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 62, normalized size = 0.8 \begin{align*}{\frac{30375\,{x}^{9}}{4}}+{\frac{127575\,{x}^{8}}{2}}+{\frac{28463805\,{x}^{7}}{112}}+{\frac{20626947\,{x}^{6}}{32}}+{\frac{379446471\,{x}^{5}}{320}}+{\frac{220950207\,{x}^{4}}{128}}+{\frac{551942075\,{x}^{3}}{256}}+{\frac{1312685491\,{x}^{2}}{512}}+{\frac{3690540955\,x}{1024}}+{\frac{298946109\,\ln \left ( 2\,x-1 \right ) }{128}}-{\frac{1096135733}{4096\,x-2048}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.37097, size = 82, normalized size = 0.99 \begin{align*} \frac{30375}{4} \, x^{9} + \frac{127575}{2} \, x^{8} + \frac{28463805}{112} \, x^{7} + \frac{20626947}{32} \, x^{6} + \frac{379446471}{320} \, x^{5} + \frac{220950207}{128} \, x^{4} + \frac{551942075}{256} \, x^{3} + \frac{1312685491}{512} \, x^{2} + \frac{3690540955}{1024} \, x - \frac{1096135733}{2048 \,{\left (2 \, x - 1\right )}} + \frac{298946109}{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 = 1.29646, size = 343, normalized size = 4.13 \begin{align*} \frac{1088640000 \, x^{10} + 8600256000 \, x^{9} + 31861382400 \, x^{8} + 74191887360 \, x^{7} + 123787657728 \, x^{6} + 162468222336 \, x^{5} + 185355446080 \, x^{4} + 213008156480 \, x^{3} + 332899764960 \, x^{2} + 167409821040 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 258337866850 \, x - 38364750655}{71680 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.126668, size = 75, normalized size = 0.9 \begin{align*} \frac{30375 x^{9}}{4} + \frac{127575 x^{8}}{2} + \frac{28463805 x^{7}}{112} + \frac{20626947 x^{6}}{32} + \frac{379446471 x^{5}}{320} + \frac{220950207 x^{4}}{128} + \frac{551942075 x^{3}}{256} + \frac{1312685491 x^{2}}{512} + \frac{3690540955 x}{1024} + \frac{298946109 \log{\left (2 x - 1 \right )}}{128} - \frac{1096135733}{4096 x - 2048} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.07389, size = 150, normalized size = 1.81 \begin{align*} \frac{1}{71680} \,{\left (2 \, x - 1\right )}^{9}{\left (\frac{27428625}{2 \, x - 1} + \frac{323475525}{{\left (2 \, x - 1\right )}^{2}} + \frac{2307572820}{{\left (2 \, x - 1\right )}^{3}} + \frac{11110625442}{{\left (2 \, x - 1\right )}^{4}} + \frac{38208385530}{{\left (2 \, x - 1\right )}^{5}} + \frac{97321773850}{{\left (2 \, x - 1\right )}^{6}} + \frac{191214919700}{{\left (2 \, x - 1\right )}^{7}} + \frac{328704835305}{{\left (2 \, x - 1\right )}^{8}} + 1063125\right )} - \frac{1096135733}{2048 \,{\left (2 \, x - 1\right )}} - \frac{298946109}{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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