Optimal. Leaf size=76 \[ \frac {99648703}{1024 (1-2 x)}+\frac {9077405 x}{16}+\frac {195497697 x^2}{512}+\frac {18842715 x^3}{64}+\frac {53086563 x^4}{256}+\frac {4750569 x^5}{40}+\frac {1597239 x^6}{32}+\frac {375435 x^7}{28}+\frac {54675 x^8}{32}+\frac {389535839 \log (1-2 x)}{1024} \]
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Rubi [A]
time = 0.03, antiderivative size = 76, normalized size of antiderivative = 1.00, 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 = {90}
\begin {gather*} \frac {54675 x^8}{32}+\frac {375435 x^7}{28}+\frac {1597239 x^6}{32}+\frac {4750569 x^5}{40}+\frac {53086563 x^4}{256}+\frac {18842715 x^3}{64}+\frac {195497697 x^2}{512}+\frac {9077405 x}{16}+\frac {99648703}{1024 (1-2 x)}+\frac {389535839 \log (1-2 x)}{1024} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^7 (3+5 x)^2}{(1-2 x)^2} \, dx &=\int \left (\frac {9077405}{16}+\frac {195497697 x}{256}+\frac {56528145 x^2}{64}+\frac {53086563 x^3}{64}+\frac {4750569 x^4}{8}+\frac {4791717 x^5}{16}+\frac {375435 x^6}{4}+\frac {54675 x^7}{4}+\frac {99648703}{512 (-1+2 x)^2}+\frac {389535839}{512 (-1+2 x)}\right ) \, dx\\ &=\frac {99648703}{1024 (1-2 x)}+\frac {9077405 x}{16}+\frac {195497697 x^2}{512}+\frac {18842715 x^3}{64}+\frac {53086563 x^4}{256}+\frac {4750569 x^5}{40}+\frac {1597239 x^6}{32}+\frac {375435 x^7}{28}+\frac {54675 x^8}{32}+\frac {389535839 \log (1-2 x)}{1024}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 69, normalized size = 0.91 \begin {gather*} \frac {96389258691-411248888662 x+215855484880 x^2+134542057440 x^3+109373775840 x^4+84861822528 x^5+53792895744 x^6+24778068480 x^7+7199020800 x^8+979776000 x^9+109070034920 (-1+2 x) \log (1-2 x)}{286720 (-1+2 x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 57, normalized size = 0.75
method | result | size |
risch | \(\frac {54675 x^{8}}{32}+\frac {375435 x^{7}}{28}+\frac {1597239 x^{6}}{32}+\frac {4750569 x^{5}}{40}+\frac {53086563 x^{4}}{256}+\frac {18842715 x^{3}}{64}+\frac {195497697 x^{2}}{512}+\frac {9077405 x}{16}-\frac {99648703}{2048 \left (-\frac {1}{2}+x \right )}+\frac {389535839 \ln \left (-1+2 x \right )}{1024}\) | \(55\) |
default | \(\frac {54675 x^{8}}{32}+\frac {375435 x^{7}}{28}+\frac {1597239 x^{6}}{32}+\frac {4750569 x^{5}}{40}+\frac {53086563 x^{4}}{256}+\frac {18842715 x^{3}}{64}+\frac {195497697 x^{2}}{512}+\frac {9077405 x}{16}-\frac {99648703}{1024 \left (-1+2 x \right )}+\frac {389535839 \ln \left (-1+2 x \right )}{1024}\) | \(57\) |
norman | \(\frac {-\frac {390125663}{512} x +\frac {385456223}{512} x^{2}+\frac {120126837}{256} x^{3}+\frac {97655157}{256} x^{4}+\frac {189423711}{640} x^{5}+\frac {30018357}{160} x^{6}+\frac {9678933}{112} x^{7}+\frac {5624235}{224} x^{8}+\frac {54675}{16} x^{9}}{-1+2 x}+\frac {389535839 \ln \left (-1+2 x \right )}{1024}\) | \(62\) |
meijerg | \(\frac {9120 x}{1-2 x}+\frac {389535839 \ln \left (1-2 x \right )}{1024}+\frac {24488 x \left (-6 x +6\right )}{3 \left (1-2 x \right )}+\frac {21945 x \left (-8 x^{2}-12 x +12\right )}{2 \left (1-2 x \right )}+\frac {6741 x \left (-40 x^{3}-40 x^{2}-60 x +60\right )}{2 \left (1-2 x \right )}+\frac {103509 x \left (-48 x^{4}-40 x^{3}-40 x^{2}-60 x +60\right )}{32 \left (1-2 x \right )}+\frac {90801 x \left (-448 x^{5}-336 x^{4}-280 x^{3}-280 x^{2}-420 x +420\right )}{320 \left (1-2 x \right )}+\frac {278721 x \left (-1280 x^{6}-896 x^{5}-672 x^{4}-560 x^{3}-560 x^{2}-840 x +840\right )}{5120 \left (1-2 x \right )}+\frac {891 x \left (-5760 x^{7}-3840 x^{6}-2688 x^{5}-2016 x^{4}-1680 x^{3}-1680 x^{2}-2520 x +2520\right )}{224 \left (1-2 x \right )}+\frac {10935 x \left (-8960 x^{8}-5760 x^{7}-3840 x^{6}-2688 x^{5}-2016 x^{4}-1680 x^{3}-1680 x^{2}-2520 x +2520\right )}{28672 \left (1-2 x \right )}\) | \(280\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 56, normalized size = 0.74 \begin {gather*} \frac {54675}{32} \, x^{8} + \frac {375435}{28} \, x^{7} + \frac {1597239}{32} \, x^{6} + \frac {4750569}{40} \, x^{5} + \frac {53086563}{256} \, x^{4} + \frac {18842715}{64} \, x^{3} + \frac {195497697}{512} \, x^{2} + \frac {9077405}{16} \, x - \frac {99648703}{1024 \, {\left (2 \, x - 1\right )}} + \frac {389535839}{1024} \, \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 = 1.53, size = 67, normalized size = 0.88 \begin {gather*} \frac {122472000 \, x^{9} + 899877600 \, x^{8} + 3097258560 \, x^{7} + 6724111968 \, x^{6} + 10607727816 \, x^{5} + 13671721980 \, x^{4} + 16817757180 \, x^{3} + 26981935610 \, x^{2} + 13633754365 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 20333387200 \, x - 3487704605}{35840 \, {\left (2 \, x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 68, normalized size = 0.89 \begin {gather*} \frac {54675 x^{8}}{32} + \frac {375435 x^{7}}{28} + \frac {1597239 x^{6}}{32} + \frac {4750569 x^{5}}{40} + \frac {53086563 x^{4}}{256} + \frac {18842715 x^{3}}{64} + \frac {195497697 x^{2}}{512} + \frac {9077405 x}{16} + \frac {389535839 \log {\left (2 x - 1 \right )}}{1024} - \frac {99648703}{2048 x - 1024} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.41, size = 102, normalized size = 1.34 \begin {gather*} \frac {1}{286720} \, {\left (2 \, x - 1\right )}^{8} {\left (\frac {45343800}{2 \, x - 1} + \frac {487438560}{{\left (2 \, x - 1\right )}^{2}} + \frac {3143702016}{{\left (2 \, x - 1\right )}^{3}} + \frac {13576070340}{{\left (2 \, x - 1\right )}^{4}} + \frac {41688082800}{{\left (2 \, x - 1\right )}^{5}} + \frac {96001584000}{{\left (2 \, x - 1\right )}^{6}} + \frac {189480773440}{{\left (2 \, x - 1\right )}^{7}} + 1913625\right )} - \frac {99648703}{1024 \, {\left (2 \, x - 1\right )}} - \frac {389535839}{1024} \, \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 = 0.05, size = 54, normalized size = 0.71 \begin {gather*} \frac {9077405\,x}{16}+\frac {389535839\,\ln \left (x-\frac {1}{2}\right )}{1024}-\frac {99648703}{2048\,\left (x-\frac {1}{2}\right )}+\frac {195497697\,x^2}{512}+\frac {18842715\,x^3}{64}+\frac {53086563\,x^4}{256}+\frac {4750569\,x^5}{40}+\frac {1597239\,x^6}{32}+\frac {375435\,x^7}{28}+\frac {54675\,x^8}{32} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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