Optimal. Leaf size=81 \[ \frac {697540921}{2048 (1-2 x)}+\frac {2330515357 x}{1024}+\frac {413355417 x^2}{256}+\frac {346239417 x^3}{256}+\frac {275757561 x^4}{256}+\frac {235268793 x^5}{320}+396738 x^6+\frac {17378631 x^7}{112}+\frac {1235655 x^8}{32}+\frac {18225 x^9}{4}+\frac {1512848491 \log (1-2 x)}{1024} \]
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Rubi [A]
time = 0.03, antiderivative size = 81, 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 {18225 x^9}{4}+\frac {1235655 x^8}{32}+\frac {17378631 x^7}{112}+396738 x^6+\frac {235268793 x^5}{320}+\frac {275757561 x^4}{256}+\frac {346239417 x^3}{256}+\frac {413355417 x^2}{256}+\frac {2330515357 x}{1024}+\frac {697540921}{2048 (1-2 x)}+\frac {1512848491 \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)^8 (3+5 x)^2}{(1-2 x)^2} \, dx &=\int \left (\frac {2330515357}{1024}+\frac {413355417 x}{128}+\frac {1038718251 x^2}{256}+\frac {275757561 x^3}{64}+\frac {235268793 x^4}{64}+2380428 x^5+\frac {17378631 x^6}{16}+\frac {1235655 x^7}{4}+\frac {164025 x^8}{4}+\frac {697540921}{1024 (-1+2 x)^2}+\frac {1512848491}{512 (-1+2 x)}\right ) \, dx\\ &=\frac {697540921}{2048 (1-2 x)}+\frac {2330515357 x}{1024}+\frac {413355417 x^2}{256}+\frac {346239417 x^3}{256}+\frac {275757561 x^4}{256}+\frac {235268793 x^5}{320}+396738 x^6+\frac {17378631 x^7}{112}+\frac {1235655 x^8}{32}+\frac {18225 x^9}{4}+\frac {1512848491 \log (1-2 x)}{1024}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 74, normalized size = 0.91 \begin {gather*} \frac {420890769939-1689637297718 x+842130532880 x^2+538127987040 x^3+466727825760 x^4+406896098112 x^5+307848957696 x^6+183016143360 x^7+77907121920 x^8+20836569600 x^9+2612736000 x^{10}+423597577480 (-1+2 x) \log (1-2 x)}{286720 (-1+2 x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 62, normalized size = 0.77
method | result | size |
risch | \(\frac {18225 x^{9}}{4}+\frac {1235655 x^{8}}{32}+\frac {17378631 x^{7}}{112}+396738 x^{6}+\frac {235268793 x^{5}}{320}+\frac {275757561 x^{4}}{256}+\frac {346239417 x^{3}}{256}+\frac {413355417 x^{2}}{256}+\frac {2330515357 x}{1024}-\frac {697540921}{4096 \left (-\frac {1}{2}+x \right )}+\frac {1512848491 \ln \left (-1+2 x \right )}{1024}\) | \(60\) |
default | \(\frac {18225 x^{9}}{4}+\frac {1235655 x^{8}}{32}+\frac {17378631 x^{7}}{112}+396738 x^{6}+\frac {235268793 x^{5}}{320}+\frac {275757561 x^{4}}{256}+\frac {346239417 x^{3}}{256}+\frac {413355417 x^{2}}{256}+\frac {2330515357 x}{1024}-\frac {697540921}{2048 \left (-1+2 x \right )}+\frac {1512848491 \ln \left (-1+2 x \right )}{1024}\) | \(62\) |
norman | \(\frac {-\frac {1514028139}{512} x +\frac {1503804523}{512} x^{2}+\frac {480471417}{256} x^{3}+\frac {416721273}{256} x^{4}+\frac {908250219}{640} x^{5}+\frac {171790713}{160} x^{6}+\frac {71490681}{112} x^{7}+\frac {60864939}{224} x^{8}+\frac {1162755}{16} x^{9}+\frac {18225}{2} x^{10}}{-1+2 x}+\frac {1512848491 \ln \left (-1+2 x \right )}{1024}\) | \(67\) |
meijerg | \(\frac {19968 x}{1-2 x}+\frac {15309 x \left (-8960 x^{8}-5760 x^{7}-3840 x^{6}-2688 x^{5}-2016 x^{4}-1680 x^{3}-1680 x^{2}-2520 x +2520\right )}{2048 \left (1-2 x \right )}+\frac {1512848491 \ln \left (1-2 x \right )}{1024}+\frac {18225 x \left (-157696 x^{9}-98560 x^{8}-63360 x^{7}-42240 x^{6}-29568 x^{5}-22176 x^{4}-18480 x^{3}-18480 x^{2}-27720 x +27720\right )}{315392 \left (1-2 x \right )}+\frac {114291 x \left (-1280 x^{6}-896 x^{5}-672 x^{4}-560 x^{3}-560 x^{2}-840 x +840\right )}{320 \left (1-2 x \right )}+\frac {350001 x \left (-5760 x^{7}-3840 x^{6}-2688 x^{5}-2016 x^{4}-1680 x^{3}-1680 x^{2}-2520 x +2520\right )}{8960 \left (1-2 x \right )}+\frac {12789 x \left (-48 x^{4}-40 x^{3}-40 x^{2}-60 x +60\right )}{1-2 x}+\frac {55971 x \left (-448 x^{5}-336 x^{4}-280 x^{3}-280 x^{2}-420 x +420\right )}{40 \left (1-2 x \right )}+\frac {31128 x \left (-8 x^{2}-12 x +12\right )}{1-2 x}+\frac {11130 x \left (-40 x^{3}-40 x^{2}-60 x +60\right )}{1-2 x}+\frac {60928 x \left (-6 x +6\right )}{3 \left (1-2 x \right )}\) | \(335\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.35, size = 61, normalized size = 0.75 \begin {gather*} \frac {18225}{4} \, x^{9} + \frac {1235655}{32} \, x^{8} + \frac {17378631}{112} \, x^{7} + 396738 \, x^{6} + \frac {235268793}{320} \, x^{5} + \frac {275757561}{256} \, x^{4} + \frac {346239417}{256} \, x^{3} + \frac {413355417}{256} \, x^{2} + \frac {2330515357}{1024} \, x - \frac {697540921}{2048 \, {\left (2 \, x - 1\right )}} + \frac {1512848491}{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 = 0.97, size = 72, normalized size = 0.89 \begin {gather*} \frac {653184000 \, x^{10} + 5209142400 \, x^{9} + 19476780480 \, x^{8} + 45754035840 \, x^{7} + 76962239424 \, x^{6} + 101724024528 \, x^{5} + 116681956440 \, x^{4} + 134531996760 \, x^{3} + 210532633220 \, x^{2} + 105899394370 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 163136074990 \, x - 24413932235}{71680 \, {\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 = 73, normalized size = 0.90 \begin {gather*} \frac {18225 x^{9}}{4} + \frac {1235655 x^{8}}{32} + \frac {17378631 x^{7}}{112} + 396738 x^{6} + \frac {235268793 x^{5}}{320} + \frac {275757561 x^{4}}{256} + \frac {346239417 x^{3}}{256} + \frac {413355417 x^{2}}{256} + \frac {2330515357 x}{1024} + \frac {1512848491 \log {\left (2 x - 1 \right )}}{1024} - \frac {697540921}{4096 x - 2048} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.24, size = 111, normalized size = 1.37 \begin {gather*} \frac {1}{286720} \, {\left (2 \, x - 1\right )}^{9} {\left (\frac {66211425}{2 \, x - 1} + \frac {785410020}{{\left (2 \, x - 1\right )}^{2}} + \frac {5635662480}{{\left (2 \, x - 1\right )}^{3}} + \frac {27294241464}{{\left (2 \, x - 1\right )}^{4}} + \frac {94415339340}{{\left (2 \, x - 1\right )}^{5}} + \frac {241909873800}{{\left (2 \, x - 1\right )}^{6}} + \frac {478116124080}{{\left (2 \, x - 1\right )}^{7}} + \frac {826787759420}{{\left (2 \, x - 1\right )}^{8}} + 2551500\right )} - \frac {697540921}{2048 \, {\left (2 \, x - 1\right )}} - \frac {1512848491}{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 = 59, normalized size = 0.73 \begin {gather*} \frac {2330515357\,x}{1024}+\frac {1512848491\,\ln \left (x-\frac {1}{2}\right )}{1024}-\frac {697540921}{4096\,\left (x-\frac {1}{2}\right )}+\frac {413355417\,x^2}{256}+\frac {346239417\,x^3}{256}+\frac {275757561\,x^4}{256}+\frac {235268793\,x^5}{320}+396738\,x^6+\frac {17378631\,x^7}{112}+\frac {1235655\,x^8}{32}+\frac {18225\,x^9}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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