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 = 0.04, antiderivative size = 69, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, 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*}
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Mathematica [A] time = 0.02, 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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fricas [A] time = 0.91, size = 62, normalized size = 0.90 \[ \frac {13996800 \, x^{8} + 95333760 \, x^{7} + 304492608 \, x^{6} + 619554096 \, x^{5} + 945299880 \, x^{4} + 1283987880 \, x^{3} + 2148763260 \, x^{2} + 1095312190 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 1563377550 \, x - 317064055}{17920 \, {\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.94, size = 93, normalized size = 1.35 \[ \frac {3}{35840} \, {\left (2 \, x - 1\right )}^{7} {\left (\frac {788130}{2 \, x - 1} + \frac {7668108}{{\left (2 \, x - 1\right )}^{2}} + \frac {44406495}{{\left (2 \, x - 1\right )}^{3}} + \frac {171431400}{{\left (2 \, x - 1\right )}^{4}} + \frac {476478450}{{\left (2 \, x - 1\right )}^{5}} + \frac {1103547620}{{\left (2 \, x - 1\right )}^{6}} + 36450\right )} - \frac {9058973}{512 \, {\left (2 \, x - 1\right )}} - \frac {15647317}{256} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 52, normalized size = 0.75 \[ \frac {10935 x^{7}}{28}+\frac {11421 x^{6}}{4}+\frac {793881 x^{5}}{80}+\frac {1423899 x^{4}}{64}+\frac {2399985 x^{3}}{64}+\frac {873207 x^{2}}{16}+\frac {22333965 x}{256}+\frac {15647317 \ln \left (2 x -1\right )}{256}-\frac {9058973}{512 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.63, size = 51, normalized size = 0.74 \[ \frac {10935}{28} \, x^{7} + \frac {11421}{4} \, x^{6} + \frac {793881}{80} \, x^{5} + \frac {1423899}{64} \, x^{4} + \frac {2399985}{64} \, x^{3} + \frac {873207}{16} \, x^{2} + \frac {22333965}{256} \, x - \frac {9058973}{512 \, {\left (2 \, x - 1\right )}} + \frac {15647317}{256} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 49, normalized size = 0.71 \[ \frac {22333965\,x}{256}+\frac {15647317\,\ln \left (x-\frac {1}{2}\right )}{256}-\frac {9058973}{1024\,\left (x-\frac {1}{2}\right )}+\frac {873207\,x^2}{16}+\frac {2399985\,x^3}{64}+\frac {1423899\,x^4}{64}+\frac {793881\,x^5}{80}+\frac {11421\,x^6}{4}+\frac {10935\,x^7}{28} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 61, normalized size = 0.88 \[ \frac {10935 x^{7}}{28} + \frac {11421 x^{6}}{4} + \frac {793881 x^{5}}{80} + \frac {1423899 x^{4}}{64} + \frac {2399985 x^{3}}{64} + \frac {873207 x^{2}}{16} + \frac {22333965 x}{256} + \frac {15647317 \log {\left (2 x - 1 \right )}}{256} - \frac {9058973}{1024 x - 512} \]
Verification of antiderivative is not currently implemented for this CAS.
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