Optimal. Leaf size=41 \[ \frac{75 x^3}{4}+\frac{795 x^2}{8}+\frac{5119 x}{16}+\frac{5929}{32 (1-2 x)}+\frac{1309}{4} \log (1-2 x) \]
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Rubi [A] time = 0.0195414, antiderivative size = 41, 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} \[ \frac{75 x^3}{4}+\frac{795 x^2}{8}+\frac{5119 x}{16}+\frac{5929}{32 (1-2 x)}+\frac{1309}{4} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^2 (3+5 x)^2}{(1-2 x)^2} \, dx &=\int \left (\frac{5119}{16}+\frac{795 x}{4}+\frac{225 x^2}{4}+\frac{5929}{16 (-1+2 x)^2}+\frac{1309}{2 (-1+2 x)}\right ) \, dx\\ &=\frac{5929}{32 (1-2 x)}+\frac{5119 x}{16}+\frac{795 x^2}{8}+\frac{75 x^3}{4}+\frac{1309}{4} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0145421, size = 41, normalized size = 1. \[ \frac{300 x^4+1440 x^3+4324 x^2-5554 x+2618 (2 x-1) \log (1-2 x)+15}{16 x-8} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 32, normalized size = 0.8 \begin{align*}{\frac{75\,{x}^{3}}{4}}+{\frac{795\,{x}^{2}}{8}}+{\frac{5119\,x}{16}}+{\frac{1309\,\ln \left ( 2\,x-1 \right ) }{4}}-{\frac{5929}{64\,x-32}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0469, size = 42, normalized size = 1.02 \begin{align*} \frac{75}{4} \, x^{3} + \frac{795}{8} \, x^{2} + \frac{5119}{16} \, x - \frac{5929}{32 \,{\left (2 \, x - 1\right )}} + \frac{1309}{4} \, \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 = 1.26461, size = 132, normalized size = 3.22 \begin{align*} \frac{1200 \, x^{4} + 5760 \, x^{3} + 17296 \, x^{2} + 10472 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 10238 \, x - 5929}{32 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.096828, size = 34, normalized size = 0.83 \begin{align*} \frac{75 x^{3}}{4} + \frac{795 x^{2}}{8} + \frac{5119 x}{16} + \frac{1309 \log{\left (2 x - 1 \right )}}{4} - \frac{5929}{64 x - 32} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.36188, size = 77, normalized size = 1.88 \begin{align*} \frac{1}{32} \,{\left (2 \, x - 1\right )}^{3}{\left (\frac{1020}{2 \, x - 1} + \frac{6934}{{\left (2 \, x - 1\right )}^{2}} + 75\right )} - \frac{5929}{32 \,{\left (2 \, x - 1\right )}} - \frac{1309}{4} \, \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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