Optimal. Leaf size=46 \[ \frac{405 x^4}{16}+144 x^3+\frac{13419 x^2}{32}+\frac{16203 x}{16}+\frac{26411}{64 (1-2 x)}+\frac{57281}{64} \log (1-2 x) \]
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Rubi [A] time = 0.0230955, antiderivative size = 46, 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} \[ \frac{405 x^4}{16}+144 x^3+\frac{13419 x^2}{32}+\frac{16203 x}{16}+\frac{26411}{64 (1-2 x)}+\frac{57281}{64} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x)^4 (3+5 x)}{(1-2 x)^2} \, dx &=\int \left (\frac{16203}{16}+\frac{13419 x}{16}+432 x^2+\frac{405 x^3}{4}+\frac{26411}{32 (-1+2 x)^2}+\frac{57281}{32 (-1+2 x)}\right ) \, dx\\ &=\frac{26411}{64 (1-2 x)}+\frac{16203 x}{16}+\frac{13419 x^2}{32}+144 x^3+\frac{405 x^4}{16}+\frac{57281}{64} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0111114, size = 49, normalized size = 1.07 \[ \frac{12960 x^5+67248 x^4+177840 x^3+411144 x^2-582198 x+229124 (2 x-1) \log (1-2 x)+55831}{256 (2 x-1)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 37, normalized size = 0.8 \begin{align*}{\frac{405\,{x}^{4}}{16}}+144\,{x}^{3}+{\frac{13419\,{x}^{2}}{32}}+{\frac{16203\,x}{16}}+{\frac{57281\,\ln \left ( 2\,x-1 \right ) }{64}}-{\frac{26411}{128\,x-64}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.37809, size = 49, normalized size = 1.07 \begin{align*} \frac{405}{16} \, x^{4} + 144 \, x^{3} + \frac{13419}{32} \, x^{2} + \frac{16203}{16} \, x - \frac{26411}{64 \,{\left (2 \, x - 1\right )}} + \frac{57281}{64} \, \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 = 1.22178, size = 153, normalized size = 3.33 \begin{align*} \frac{3240 \, x^{5} + 16812 \, x^{4} + 44460 \, x^{3} + 102786 \, x^{2} + 57281 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 64812 \, x - 26411}{64 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.106839, size = 39, normalized size = 0.85 \begin{align*} \frac{405 x^{4}}{16} + 144 x^{3} + \frac{13419 x^{2}}{32} + \frac{16203 x}{16} + \frac{57281 \log{\left (2 x - 1 \right )}}{64} - \frac{26411}{128 x - 64} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.20702, size = 89, normalized size = 1.93 \begin{align*} \frac{3}{256} \,{\left (2 \, x - 1\right )}^{4}{\left (\frac{2076}{2 \, x - 1} + \frac{14364}{{\left (2 \, x - 1\right )}^{2}} + \frac{66248}{{\left (2 \, x - 1\right )}^{3}} + 135\right )} - \frac{26411}{64 \,{\left (2 \, x - 1\right )}} - \frac{57281}{64} \, \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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