Optimal. Leaf size=73 \[ \frac {14235529}{1024 (1-2 x)^2}-\frac {12386759}{128 (1-2 x)}-\frac {39980457 x}{256}-\frac {17700255 x^2}{256}-\frac {1024389 x^3}{32}-\frac {770067 x^4}{64}-\frac {48843 x^5}{16}-\frac {6075 x^6}{16}-\frac {18859855}{128} \log (1-2 x) \]
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Rubi [A]
time = 0.03, antiderivative size = 73, 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 {6075 x^6}{16}-\frac {48843 x^5}{16}-\frac {770067 x^4}{64}-\frac {1024389 x^3}{32}-\frac {17700255 x^2}{256}-\frac {39980457 x}{256}-\frac {12386759}{128 (1-2 x)}+\frac {14235529}{1024 (1-2 x)^2}-\frac {18859855}{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)^6 (3+5 x)^2}{(1-2 x)^3} \, dx &=\int \left (-\frac {39980457}{256}-\frac {17700255 x}{128}-\frac {3073167 x^2}{32}-\frac {770067 x^3}{16}-\frac {244215 x^4}{16}-\frac {18225 x^5}{8}-\frac {14235529}{256 (-1+2 x)^3}-\frac {12386759}{64 (-1+2 x)^2}-\frac {18859855}{64 (-1+2 x)}\right ) \, dx\\ &=\frac {14235529}{1024 (1-2 x)^2}-\frac {12386759}{128 (1-2 x)}-\frac {39980457 x}{256}-\frac {17700255 x^2}{256}-\frac {1024389 x^3}{32}-\frac {770067 x^4}{64}-\frac {48843 x^5}{16}-\frac {6075 x^6}{16}-\frac {18859855}{128} \log (1-2 x)\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 66, normalized size = 0.90 \begin {gather*} -\frac {-8887005+186131948 x-489708252 x^2+194631840 x^3+82201680 x^4+42481728 x^5+18584640 x^6+5474304 x^7+777600 x^8+75439420 (1-2 x)^2 \log (1-2 x)}{512 (1-2 x)^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 56, normalized size = 0.77
method | result | size |
risch | \(-\frac {6075 x^{6}}{16}-\frac {48843 x^{5}}{16}-\frac {770067 x^{4}}{64}-\frac {1024389 x^{3}}{32}-\frac {17700255 x^{2}}{256}-\frac {39980457 x}{256}+\frac {\frac {12386759 x}{64}-\frac {84858543}{1024}}{\left (-1+2 x \right )^{2}}-\frac {18859855 \ln \left (-1+2 x \right )}{128}\) | \(52\) |
default | \(-\frac {6075 x^{6}}{16}-\frac {48843 x^{5}}{16}-\frac {770067 x^{4}}{64}-\frac {1024389 x^{3}}{32}-\frac {17700255 x^{2}}{256}-\frac {39980457 x}{256}+\frac {12386759}{128 \left (-1+2 x \right )}+\frac {14235529}{1024 \left (-1+2 x \right )^{2}}-\frac {18859855 \ln \left (-1+2 x \right )}{128}\) | \(56\) |
norman | \(\frac {-\frac {18822991}{64} x +\frac {56770029}{64} x^{2}-\frac {6082245}{16} x^{3}-\frac {5137605}{32} x^{4}-\frac {663777}{8} x^{5}-\frac {290385}{8} x^{6}-10692 x^{7}-\frac {6075}{4} x^{8}}{\left (-1+2 x \right )^{2}}-\frac {18859855 \ln \left (-1+2 x \right )}{128}\) | \(57\) |
meijerg | \(\frac {288 x \left (2-2 x \right )}{\left (1-2 x \right )^{2}}+\frac {3552 x^{2}}{\left (1-2 x \right )^{2}}-\frac {4790 x \left (-18 x +6\right )}{3 \left (1-2 x \right )^{2}}-\frac {18859855 \ln \left (1-2 x \right )}{128}-\frac {3690 x \left (16 x^{2}-36 x +12\right )}{\left (1-2 x \right )^{2}}-\frac {11367 x \left (40 x^{3}+80 x^{2}-180 x +60\right )}{8 \left (1-2 x \right )^{2}}-\frac {23337 x \left (32 x^{4}+40 x^{3}+80 x^{2}-180 x +60\right )}{16 \left (1-2 x \right )^{2}}-\frac {215541 x \left (224 x^{5}+224 x^{4}+280 x^{3}+560 x^{2}-1260 x +420\right )}{1792 \left (1-2 x \right )^{2}}-\frac {9477 x \left (512 x^{6}+448 x^{5}+448 x^{4}+560 x^{3}+1120 x^{2}-2520 x +840\right )}{512 \left (1-2 x \right )^{2}}-\frac {405 x \left (1920 x^{7}+1536 x^{6}+1344 x^{5}+1344 x^{4}+1680 x^{3}+3360 x^{2}-7560 x +2520\right )}{512 \left (1-2 x \right )^{2}}\) | \(247\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 56, normalized size = 0.77 \begin {gather*} -\frac {6075}{16} \, x^{6} - \frac {48843}{16} \, x^{5} - \frac {770067}{64} \, x^{4} - \frac {1024389}{32} \, x^{3} - \frac {17700255}{256} \, x^{2} - \frac {39980457}{256} \, x + \frac {184877 \, {\left (1072 \, x - 459\right )}}{1024 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {18859855}{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 = 0.41, size = 72, normalized size = 0.99 \begin {gather*} -\frac {1555200 \, x^{8} + 10948608 \, x^{7} + 37169280 \, x^{6} + 84963456 \, x^{5} + 164403360 \, x^{4} + 389263680 \, x^{3} - 568886292 \, x^{2} + 150878840 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 38266316 \, x + 84858543}{1024 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 65, normalized size = 0.89 \begin {gather*} - \frac {6075 x^{6}}{16} - \frac {48843 x^{5}}{16} - \frac {770067 x^{4}}{64} - \frac {1024389 x^{3}}{32} - \frac {17700255 x^{2}}{256} - \frac {39980457 x}{256} - \frac {84858543 - 198188144 x}{4096 x^{2} - 4096 x + 1024} - \frac {18859855 \log {\left (2 x - 1 \right )}}{128} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.54, size = 52, normalized size = 0.71 \begin {gather*} -\frac {6075}{16} \, x^{6} - \frac {48843}{16} \, x^{5} - \frac {770067}{64} \, x^{4} - \frac {1024389}{32} \, x^{3} - \frac {17700255}{256} \, x^{2} - \frac {39980457}{256} \, x + \frac {184877 \, {\left (1072 \, x - 459\right )}}{1024 \, {\left (2 \, x - 1\right )}^{2}} - \frac {18859855}{128} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 51, normalized size = 0.70 \begin {gather*} \frac {\frac {12386759\,x}{256}-\frac {84858543}{4096}}{x^2-x+\frac {1}{4}}-\frac {18859855\,\ln \left (x-\frac {1}{2}\right )}{128}-\frac {39980457\,x}{256}-\frac {17700255\,x^2}{256}-\frac {1024389\,x^3}{32}-\frac {770067\,x^4}{64}-\frac {48843\,x^5}{16}-\frac {6075\,x^6}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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