Optimal. Leaf size=66 \[ -\frac{729 x^5}{8}-\frac{44469 x^4}{64}-\frac{10611 x^3}{4}-\frac{461835 x^2}{64}-\frac{2431647 x}{128}-\frac{3916031}{256 (1-2 x)}+\frac{1294139}{512 (1-2 x)^2}-\frac{5078115}{256} \log (1-2 x) \]
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Rubi [A] time = 0.0350226, antiderivative size = 66, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ -\frac{729 x^5}{8}-\frac{44469 x^4}{64}-\frac{10611 x^3}{4}-\frac{461835 x^2}{64}-\frac{2431647 x}{128}-\frac{3916031}{256 (1-2 x)}+\frac{1294139}{512 (1-2 x)^2}-\frac{5078115}{256} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x)^6 (3+5 x)}{(1-2 x)^3} \, dx &=\int \left (-\frac{2431647}{128}-\frac{461835 x}{32}-\frac{31833 x^2}{4}-\frac{44469 x^3}{16}-\frac{3645 x^4}{8}-\frac{1294139}{128 (-1+2 x)^3}-\frac{3916031}{128 (-1+2 x)^2}-\frac{5078115}{128 (-1+2 x)}\right ) \, dx\\ &=\frac{1294139}{512 (1-2 x)^2}-\frac{3916031}{256 (1-2 x)}-\frac{2431647 x}{128}-\frac{461835 x^2}{64}-\frac{10611 x^3}{4}-\frac{44469 x^4}{64}-\frac{729 x^5}{8}-\frac{5078115}{256} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0164457, size = 61, normalized size = 0.92 \[ -\frac{373248 x^7+2472768 x^6+8112960 x^5+19403280 x^4+50971680 x^3-118266804 x^2+35968388 x+20312460 (1-2 x)^2 \log (1-2 x)+1114981}{1024 (1-2 x)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 51, normalized size = 0.8 \begin{align*} -{\frac{729\,{x}^{5}}{8}}-{\frac{44469\,{x}^{4}}{64}}-{\frac{10611\,{x}^{3}}{4}}-{\frac{461835\,{x}^{2}}{64}}-{\frac{2431647\,x}{128}}-{\frac{5078115\,\ln \left ( 2\,x-1 \right ) }{256}}+{\frac{1294139}{512\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{3916031}{512\,x-256}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06351, size = 69, normalized size = 1.05 \begin{align*} -\frac{729}{8} \, x^{5} - \frac{44469}{64} \, x^{4} - \frac{10611}{4} \, x^{3} - \frac{461835}{64} \, x^{2} - \frac{2431647}{128} \, x + \frac{16807 \,{\left (932 \, x - 389\right )}}{512 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{5078115}{256} \, \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 = 1.44726, size = 236, normalized size = 3.58 \begin{align*} -\frac{186624 \, x^{7} + 1236384 \, x^{6} + 4056480 \, x^{5} + 9701640 \, x^{4} + 25485840 \, x^{3} - 35211672 \, x^{2} + 10156230 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 5937536 \, x + 6537923}{512 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.128977, size = 56, normalized size = 0.85 \begin{align*} - \frac{729 x^{5}}{8} - \frac{44469 x^{4}}{64} - \frac{10611 x^{3}}{4} - \frac{461835 x^{2}}{64} - \frac{2431647 x}{128} + \frac{15664124 x - 6537923}{2048 x^{2} - 2048 x + 512} - \frac{5078115 \log{\left (2 x - 1 \right )}}{256} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.27244, size = 63, normalized size = 0.95 \begin{align*} -\frac{729}{8} \, x^{5} - \frac{44469}{64} \, x^{4} - \frac{10611}{4} \, x^{3} - \frac{461835}{64} \, x^{2} - \frac{2431647}{128} \, x + \frac{16807 \,{\left (932 \, x - 389\right )}}{512 \,{\left (2 \, x - 1\right )}^{2}} - \frac{5078115}{256} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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