Optimal. Leaf size=69 \[ \frac{10935 x^7}{28}+\frac{11421 x^6}{4}+\frac{793881 x^5}{80}+\frac{1423899 x^4}{64}+\frac{2399985 x^3}{64}+\frac{873207 x^2}{16}+\frac{22333965 x}{256}+\frac{9058973}{512 (1-2 x)}+\frac{15647317}{256} \log (1-2 x) \]
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Rubi [A] time = 0.0366485, antiderivative size = 69, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ \frac{10935 x^7}{28}+\frac{11421 x^6}{4}+\frac{793881 x^5}{80}+\frac{1423899 x^4}{64}+\frac{2399985 x^3}{64}+\frac{873207 x^2}{16}+\frac{22333965 x}{256}+\frac{9058973}{512 (1-2 x)}+\frac{15647317}{256} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x)^7 (3+5 x)}{(1-2 x)^2} \, dx &=\int \left (\frac{22333965}{256}+\frac{873207 x}{8}+\frac{7199955 x^2}{64}+\frac{1423899 x^3}{16}+\frac{793881 x^4}{16}+\frac{34263 x^5}{2}+\frac{10935 x^6}{4}+\frac{9058973}{256 (-1+2 x)^2}+\frac{15647317}{128 (-1+2 x)}\right ) \, dx\\ &=\frac{9058973}{512 (1-2 x)}+\frac{22333965 x}{256}+\frac{873207 x^2}{16}+\frac{2399985 x^3}{64}+\frac{1423899 x^4}{64}+\frac{793881 x^5}{80}+\frac{11421 x^6}{4}+\frac{10935 x^7}{28}+\frac{15647317}{256} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0133038, size = 64, normalized size = 0.93 \[ \frac{27993600 x^8+190667520 x^7+608985216 x^6+1239108192 x^5+1890599760 x^4+2567975760 x^3+4297526520 x^2-7692818118 x+2190624380 (2 x-1) \log (1-2 x)+1648903399}{35840 (2 x-1)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 52, normalized size = 0.8 \begin{align*}{\frac{10935\,{x}^{7}}{28}}+{\frac{11421\,{x}^{6}}{4}}+{\frac{793881\,{x}^{5}}{80}}+{\frac{1423899\,{x}^{4}}{64}}+{\frac{2399985\,{x}^{3}}{64}}+{\frac{873207\,{x}^{2}}{16}}+{\frac{22333965\,x}{256}}+{\frac{15647317\,\ln \left ( 2\,x-1 \right ) }{256}}-{\frac{9058973}{1024\,x-512}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.02203, size = 69, normalized size = 1. \begin{align*} \frac{10935}{28} \, x^{7} + \frac{11421}{4} \, x^{6} + \frac{793881}{80} \, x^{5} + \frac{1423899}{64} \, x^{4} + \frac{2399985}{64} \, x^{3} + \frac{873207}{16} \, x^{2} + \frac{22333965}{256} \, x - \frac{9058973}{512 \,{\left (2 \, x - 1\right )}} + \frac{15647317}{256} \, \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 = 1.19136, size = 262, normalized size = 3.8 \begin{align*} \frac{13996800 \, x^{8} + 95333760 \, x^{7} + 304492608 \, x^{6} + 619554096 \, x^{5} + 945299880 \, x^{4} + 1283987880 \, x^{3} + 2148763260 \, x^{2} + 1095312190 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 1563377550 \, x - 317064055}{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 = 0.112001, size = 61, normalized size = 0.88 \begin{align*} \frac{10935 x^{7}}{28} + \frac{11421 x^{6}}{4} + \frac{793881 x^{5}}{80} + \frac{1423899 x^{4}}{64} + \frac{2399985 x^{3}}{64} + \frac{873207 x^{2}}{16} + \frac{22333965 x}{256} + \frac{15647317 \log{\left (2 x - 1 \right )}}{256} - \frac{9058973}{1024 x - 512} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.83046, size = 126, normalized size = 1.83 \begin{align*} \frac{3}{35840} \,{\left (2 \, x - 1\right )}^{7}{\left (\frac{788130}{2 \, x - 1} + \frac{7668108}{{\left (2 \, x - 1\right )}^{2}} + \frac{44406495}{{\left (2 \, x - 1\right )}^{3}} + \frac{171431400}{{\left (2 \, x - 1\right )}^{4}} + \frac{476478450}{{\left (2 \, x - 1\right )}^{5}} + \frac{1103547620}{{\left (2 \, x - 1\right )}^{6}} + 36450\right )} - \frac{9058973}{512 \,{\left (2 \, x - 1\right )}} - \frac{15647317}{256} \, \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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