Optimal. Leaf size=83 \[ \frac {1096135733}{2048 (1-2 x)}+\frac {3690540955 x}{1024}+\frac {1312685491 x^2}{512}+\frac {551942075 x^3}{256}+\frac {220950207 x^4}{128}+\frac {379446471 x^5}{320}+\frac {20626947 x^6}{32}+\frac {28463805 x^7}{112}+\frac {127575 x^8}{2}+\frac {30375 x^9}{4}+\frac {298946109}{128} \log (1-2 x) \]
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Rubi [A]
time = 0.03, antiderivative size = 83, 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 {30375 x^9}{4}+\frac {127575 x^8}{2}+\frac {28463805 x^7}{112}+\frac {20626947 x^6}{32}+\frac {379446471 x^5}{320}+\frac {220950207 x^4}{128}+\frac {551942075 x^3}{256}+\frac {1312685491 x^2}{512}+\frac {3690540955 x}{1024}+\frac {1096135733}{2048 (1-2 x)}+\frac {298946109}{128} \log (1-2 x) \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)^3}{(1-2 x)^2} \, dx &=\int \left (\frac {3690540955}{1024}+\frac {1312685491 x}{256}+\frac {1655826225 x^2}{256}+\frac {220950207 x^3}{32}+\frac {379446471 x^4}{64}+\frac {61880841 x^5}{16}+\frac {28463805 x^6}{16}+510300 x^7+\frac {273375 x^8}{4}+\frac {1096135733}{1024 (-1+2 x)^2}+\frac {298946109}{64 (-1+2 x)}\right ) \, dx\\ &=\frac {1096135733}{2048 (1-2 x)}+\frac {3690540955 x}{1024}+\frac {1312685491 x^2}{512}+\frac {551942075 x^3}{256}+\frac {220950207 x^4}{128}+\frac {379446471 x^5}{320}+\frac {20626947 x^6}{32}+\frac {28463805 x^7}{112}+\frac {127575 x^8}{2}+\frac {30375 x^9}{4}+\frac {298946109}{128} \log (1-2 x)\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 74, normalized size = 0.89 \begin {gather*} \frac {167338715917-669744799994 x+332899764960 x^2+213008156480 x^3+185355446080 x^4+162468222336 x^5+123787657728 x^6+74191887360 x^7+31861382400 x^8+8600256000 x^9+1088640000 x^{10}+167409821040 (-1+2 x) \log (1-2 x)}{71680 (-1+2 x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 62, normalized size = 0.75
method | result | size |
risch | \(\frac {30375 x^{9}}{4}+\frac {127575 x^{8}}{2}+\frac {28463805 x^{7}}{112}+\frac {20626947 x^{6}}{32}+\frac {379446471 x^{5}}{320}+\frac {220950207 x^{4}}{128}+\frac {551942075 x^{3}}{256}+\frac {1312685491 x^{2}}{512}+\frac {3690540955 x}{1024}-\frac {1096135733}{4096 \left (-\frac {1}{2}+x \right )}+\frac {298946109 \ln \left (-1+2 x \right )}{128}\) | \(60\) |
default | \(\frac {30375 x^{9}}{4}+\frac {127575 x^{8}}{2}+\frac {28463805 x^{7}}{112}+\frac {20626947 x^{6}}{32}+\frac {379446471 x^{5}}{320}+\frac {220950207 x^{4}}{128}+\frac {551942075 x^{3}}{256}+\frac {1312685491 x^{2}}{512}+\frac {3690540955 x}{1024}-\frac {1096135733}{2048 \left (-1+2 x \right )}+\frac {298946109 \ln \left (-1+2 x \right )}{128}\) | \(62\) |
norman | \(\frac {-\frac {299167293}{64} x +\frac {297231933}{64} x^{2}+\frac {95092927}{32} x^{3}+\frac {82747967}{32} x^{4}+\frac {181326141}{80} x^{5}+\frac {34538967}{20} x^{6}+\frac {14490603}{14} x^{7}+\frac {24891705}{56} x^{8}+\frac {479925}{4} x^{9}+\frac {30375}{2} x^{10}}{-1+2 x}+\frac {298946109 \ln \left (-1+2 x \right )}{128}\) | \(67\) |
meijerg | \(\frac {30240 x}{1-2 x}+\frac {30375 x \left (-157696 x^{9}-98560 x^{8}-63360 x^{7}-42240 x^{6}-29568 x^{5}-22176 x^{4}-18480 x^{3}-18480 x^{2}-27720 x +27720\right )}{315392 \left (1-2 x \right )}+\frac {298946109 \ln \left (1-2 x \right )}{128}+\frac {353565 x \left (-8960 x^{8}-5760 x^{7}-3840 x^{6}-2688 x^{5}-2016 x^{4}-1680 x^{3}-1680 x^{2}-2520 x +2520\right )}{28672 \left (1-2 x \right )}+\frac {114291 x \left (-5760 x^{7}-3840 x^{6}-2688 x^{5}-2016 x^{4}-1680 x^{3}-1680 x^{2}-2520 x +2520\right )}{1792 \left (1-2 x \right )}+\frac {2954853 x \left (-1280 x^{6}-896 x^{5}-672 x^{4}-560 x^{3}-560 x^{2}-840 x +840\right )}{5120 \left (1-2 x \right )}+\frac {34853 x \left (-40 x^{3}-40 x^{2}-60 x +60\right )}{2 \left (1-2 x \right )}+\frac {647577 x \left (-48 x^{4}-40 x^{3}-40 x^{2}-60 x +60\right )}{32 \left (1-2 x \right )}+\frac {716013 x \left (-448 x^{5}-336 x^{4}-280 x^{3}-280 x^{2}-420 x +420\right )}{320 \left (1-2 x \right )}+\frac {31128 x \left (-6 x +6\right )}{1-2 x}+\frac {96445 x \left (-8 x^{2}-12 x +12\right )}{2 \left (1-2 x \right )}\) | \(335\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 61, normalized size = 0.73 \begin {gather*} \frac {30375}{4} \, x^{9} + \frac {127575}{2} \, x^{8} + \frac {28463805}{112} \, x^{7} + \frac {20626947}{32} \, x^{6} + \frac {379446471}{320} \, x^{5} + \frac {220950207}{128} \, x^{4} + \frac {551942075}{256} \, x^{3} + \frac {1312685491}{512} \, x^{2} + \frac {3690540955}{1024} \, x - \frac {1096135733}{2048 \, {\left (2 \, x - 1\right )}} + \frac {298946109}{128} \, \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 = 0.50, size = 72, normalized size = 0.87 \begin {gather*} \frac {1088640000 \, x^{10} + 8600256000 \, x^{9} + 31861382400 \, x^{8} + 74191887360 \, x^{7} + 123787657728 \, x^{6} + 162468222336 \, x^{5} + 185355446080 \, x^{4} + 213008156480 \, x^{3} + 332899764960 \, x^{2} + 167409821040 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 258337866850 \, x - 38364750655}{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 = 0.08, size = 75, normalized size = 0.90 \begin {gather*} \frac {30375 x^{9}}{4} + \frac {127575 x^{8}}{2} + \frac {28463805 x^{7}}{112} + \frac {20626947 x^{6}}{32} + \frac {379446471 x^{5}}{320} + \frac {220950207 x^{4}}{128} + \frac {551942075 x^{3}}{256} + \frac {1312685491 x^{2}}{512} + \frac {3690540955 x}{1024} + \frac {298946109 \log {\left (2 x - 1 \right )}}{128} - \frac {1096135733}{4096 x - 2048} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.80, size = 111, normalized size = 1.34 \begin {gather*} \frac {1}{71680} \, {\left (2 \, x - 1\right )}^{9} {\left (\frac {27428625}{2 \, x - 1} + \frac {323475525}{{\left (2 \, x - 1\right )}^{2}} + \frac {2307572820}{{\left (2 \, x - 1\right )}^{3}} + \frac {11110625442}{{\left (2 \, x - 1\right )}^{4}} + \frac {38208385530}{{\left (2 \, x - 1\right )}^{5}} + \frac {97321773850}{{\left (2 \, x - 1\right )}^{6}} + \frac {191214919700}{{\left (2 \, x - 1\right )}^{7}} + \frac {328704835305}{{\left (2 \, x - 1\right )}^{8}} + 1063125\right )} - \frac {1096135733}{2048 \, {\left (2 \, x - 1\right )}} - \frac {298946109}{128} \, \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 = 0.06, size = 59, normalized size = 0.71 \begin {gather*} \frac {3690540955\,x}{1024}+\frac {298946109\,\ln \left (x-\frac {1}{2}\right )}{128}-\frac {1096135733}{4096\,\left (x-\frac {1}{2}\right )}+\frac {1312685491\,x^2}{512}+\frac {551942075\,x^3}{256}+\frac {220950207\,x^4}{128}+\frac {379446471\,x^5}{320}+\frac {20626947\,x^6}{32}+\frac {28463805\,x^7}{112}+\frac {127575\,x^8}{2}+\frac {30375\,x^9}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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