Optimal. Leaf size=90 \[ \frac{164025 x^{10}}{8}+\frac{370575 x^9}{2}+\frac{101721015 x^8}{128}+\frac{242570133 x^7}{112}+\frac{544462047 x^6}{128}+\frac{260574273 x^5}{40}+\frac{8502681987 x^4}{1024}+\frac{2416569641 x^3}{256}+\frac{21573106793 x^2}{2048}+\frac{7277894263 x}{512}+\frac{7672950131}{4096 (1-2 x)}+\frac{36770371407 \log (1-2 x)}{4096} \]
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Rubi [A] time = 0.0513533, antiderivative size = 90, normalized size of antiderivative = 1., 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 = {88} \[ \frac{164025 x^{10}}{8}+\frac{370575 x^9}{2}+\frac{101721015 x^8}{128}+\frac{242570133 x^7}{112}+\frac{544462047 x^6}{128}+\frac{260574273 x^5}{40}+\frac{8502681987 x^4}{1024}+\frac{2416569641 x^3}{256}+\frac{21573106793 x^2}{2048}+\frac{7277894263 x}{512}+\frac{7672950131}{4096 (1-2 x)}+\frac{36770371407 \log (1-2 x)}{4096} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^8 (3+5 x)^3}{(1-2 x)^2} \, dx &=\int \left (\frac{7277894263}{512}+\frac{21573106793 x}{1024}+\frac{7249708923 x^2}{256}+\frac{8502681987 x^3}{256}+\frac{260574273 x^4}{8}+\frac{1633386141 x^5}{64}+\frac{242570133 x^6}{16}+\frac{101721015 x^7}{16}+\frac{3335175 x^8}{2}+\frac{820125 x^9}{4}+\frac{7672950131}{2048 (-1+2 x)^2}+\frac{36770371407}{2048 (-1+2 x)}\right ) \, dx\\ &=\frac{7672950131}{4096 (1-2 x)}+\frac{7277894263 x}{512}+\frac{21573106793 x^2}{2048}+\frac{2416569641 x^3}{256}+\frac{8502681987 x^4}{1024}+\frac{260574273 x^5}{40}+\frac{544462047 x^6}{128}+\frac{242570133 x^7}{112}+\frac{101721015 x^8}{128}+\frac{370575 x^9}{2}+\frac{164025 x^{10}}{8}+\frac{36770371407 \log (1-2 x)}{4096}\\ \end{align*}
Mathematica [A] time = 0.0191604, size = 79, normalized size = 0.88 \[ \frac{47029248000 x^{11}+401490432000 x^{10}+1610338060800 x^9+4056416029440 x^8+7272841720320 x^7+10063991169792 x^6+11574822095424 x^5+12129460157920 x^4+13335647616480 x^3+20524026494160 x^2-43208575854086 x+10295703993960 (2 x-1) \log (1-2 x)+11304620315803}{1146880 (2 x-1)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 67, normalized size = 0.7 \begin{align*}{\frac{164025\,{x}^{10}}{8}}+{\frac{370575\,{x}^{9}}{2}}+{\frac{101721015\,{x}^{8}}{128}}+{\frac{242570133\,{x}^{7}}{112}}+{\frac{544462047\,{x}^{6}}{128}}+{\frac{260574273\,{x}^{5}}{40}}+{\frac{8502681987\,{x}^{4}}{1024}}+{\frac{2416569641\,{x}^{3}}{256}}+{\frac{21573106793\,{x}^{2}}{2048}}+{\frac{7277894263\,x}{512}}+{\frac{36770371407\,\ln \left ( 2\,x-1 \right ) }{4096}}-{\frac{7672950131}{8192\,x-4096}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03926, size = 89, normalized size = 0.99 \begin{align*} \frac{164025}{8} \, x^{10} + \frac{370575}{2} \, x^{9} + \frac{101721015}{128} \, x^{8} + \frac{242570133}{112} \, x^{7} + \frac{544462047}{128} \, x^{6} + \frac{260574273}{40} \, x^{5} + \frac{8502681987}{1024} \, x^{4} + \frac{2416569641}{256} \, x^{3} + \frac{21573106793}{2048} \, x^{2} + \frac{7277894263}{512} \, x - \frac{7672950131}{4096 \,{\left (2 \, x - 1\right )}} + \frac{36770371407}{4096} \, \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 = 1.26225, size = 386, normalized size = 4.29 \begin{align*} \frac{5878656000 \, x^{11} + 50186304000 \, x^{10} + 201292257600 \, x^{9} + 507052003680 \, x^{8} + 909105215040 \, x^{7} + 1257998896224 \, x^{6} + 1446852761928 \, x^{5} + 1516182519740 \, x^{4} + 1666955952060 \, x^{3} + 2565503311770 \, x^{2} + 1286962999245 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 2037810393640 \, x - 268553254585}{143360 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.12369, size = 82, normalized size = 0.91 \begin{align*} \frac{164025 x^{10}}{8} + \frac{370575 x^{9}}{2} + \frac{101721015 x^{8}}{128} + \frac{242570133 x^{7}}{112} + \frac{544462047 x^{6}}{128} + \frac{260574273 x^{5}}{40} + \frac{8502681987 x^{4}}{1024} + \frac{2416569641 x^{3}}{256} + \frac{21573106793 x^{2}}{2048} + \frac{7277894263 x}{512} + \frac{36770371407 \log{\left (2 x - 1 \right )}}{4096} - \frac{7672950131}{8192 x - 4096} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.33903, size = 162, normalized size = 1.8 \begin{align*} \frac{1}{1146880} \,{\left (2 \, x - 1\right )}^{10}{\left (\frac{644679000}{2 \, x - 1} + \frac{8328989025}{{\left (2 \, x - 1\right )}^{2}} + \frac{65584698840}{{\left (2 \, x - 1\right )}^{3}} + \frac{351436586760}{{\left (2 \, x - 1\right )}^{4}} + \frac{1355796026928}{{\left (2 \, x - 1\right )}^{5}} + \frac{3891461518980}{{\left (2 \, x - 1\right )}^{6}} + \frac{8509458050800}{{\left (2 \, x - 1\right )}^{7}} + \frac{14652493526860}{{\left (2 \, x - 1\right )}^{8}} + \frac{22425306482040}{{\left (2 \, x - 1\right )}^{9}} + 22963500\right )} - \frac{7672950131}{4096 \,{\left (2 \, x - 1\right )}} - \frac{36770371407}{4096} \, \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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