Optimal. Leaf size=69 \[ \frac {9058973}{512 (1-2 x)}+\frac {22333965 x}{256}+\frac {873207 x^2}{16}+\frac {2399985 x^3}{64}+\frac {1423899 x^4}{64}+\frac {793881 x^5}{80}+\frac {11421 x^6}{4}+\frac {10935 x^7}{28}+\frac {15647317}{256} \log (1-2 x) \]
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Rubi [A]
time = 0.02, 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 = {78}
\begin {gather*} \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) \end {gather*}
Antiderivative was successfully verified.
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Rule 78
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 = 0.01, size = 64, normalized size = 0.93 \begin {gather*} \frac {1648903399-7692818118 x+4297526520 x^2+2567975760 x^3+1890599760 x^4+1239108192 x^5+608985216 x^6+190667520 x^7+27993600 x^8+2190624380 (-1+2 x) \log (1-2 x)}{35840 (-1+2 x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 52, normalized size = 0.75
method | result | size |
risch | \(\frac {10935 x^{7}}{28}+\frac {11421 x^{6}}{4}+\frac {793881 x^{5}}{80}+\frac {1423899 x^{4}}{64}+\frac {2399985 x^{3}}{64}+\frac {873207 x^{2}}{16}+\frac {22333965 x}{256}-\frac {9058973}{1024 \left (-\frac {1}{2}+x \right )}+\frac {15647317 \ln \left (-1+2 x \right )}{256}\) | \(50\) |
default | \(\frac {10935 x^{7}}{28}+\frac {11421 x^{6}}{4}+\frac {793881 x^{5}}{80}+\frac {1423899 x^{4}}{64}+\frac {2399985 x^{3}}{64}+\frac {873207 x^{2}}{16}+\frac {22333965 x}{256}-\frac {9058973}{512 \left (-1+2 x \right )}+\frac {15647317 \ln \left (-1+2 x \right )}{256}\) | \(52\) |
norman | \(\frac {-\frac {15696469}{128} x +\frac {15348309}{128} x^{2}+\frac {4585671}{64} x^{3}+\frac {3376071}{64} x^{4}+\frac {5531733}{160} x^{5}+\frac {679671}{40} x^{6}+\frac {148959}{28} x^{7}+\frac {10935}{14} x^{8}}{-1+2 x}+\frac {15647317 \ln \left (-1+2 x \right )}{256}\) | \(57\) |
meijerg | \(\frac {2720 x}{1-2 x}+\frac {15647317 \ln \left (1-2 x \right )}{256}+\frac {2072 x \left (-6 x +6\right )}{1-2 x}+\frac {4725 x \left (-8 x^{2}-12 x +12\right )}{2 \left (1-2 x \right )}+\frac {1197 x \left (-40 x^{3}-40 x^{2}-60 x +60\right )}{2 \left (1-2 x \right )}+\frac {14553 x \left (-48 x^{4}-40 x^{3}-40 x^{2}-60 x +60\right )}{32 \left (1-2 x \right )}+\frac {9477 x \left (-448 x^{5}-336 x^{4}-280 x^{3}-280 x^{2}-420 x +420\right )}{320 \left (1-2 x \right )}+\frac {19197 x \left (-1280 x^{6}-896 x^{5}-672 x^{4}-560 x^{3}-560 x^{2}-840 x +840\right )}{5120 \left (1-2 x \right )}+\frac {243 x \left (-5760 x^{7}-3840 x^{6}-2688 x^{5}-2016 x^{4}-1680 x^{3}-1680 x^{2}-2520 x +2520\right )}{1792 \left (1-2 x \right )}\) | \(230\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 51, normalized size = 0.74 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 2.03, size = 62, normalized size = 0.90 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 61, normalized size = 0.88 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.36, size = 93, normalized size = 1.35 \begin {gather*} \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 {gather*}
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 \begin {gather*} \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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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