Optimal. Leaf size=53 \[ \frac{9}{8} (1-2 x)^{5/2}-\frac{103}{8} (1-2 x)^{3/2}+\frac{707}{8} \sqrt{1-2 x}+\frac{539}{8 \sqrt{1-2 x}} \]
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Rubi [A] time = 0.0098294, antiderivative size = 53, 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 = {77} \[ \frac{9}{8} (1-2 x)^{5/2}-\frac{103}{8} (1-2 x)^{3/2}+\frac{707}{8} \sqrt{1-2 x}+\frac{539}{8 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x)^2 (3+5 x)}{(1-2 x)^{3/2}} \, dx &=\int \left (\frac{539}{8 (1-2 x)^{3/2}}-\frac{707}{8 \sqrt{1-2 x}}+\frac{309}{8} \sqrt{1-2 x}-\frac{45}{8} (1-2 x)^{3/2}\right ) \, dx\\ &=\frac{539}{8 \sqrt{1-2 x}}+\frac{707}{8} \sqrt{1-2 x}-\frac{103}{8} (1-2 x)^{3/2}+\frac{9}{8} (1-2 x)^{5/2}\\ \end{align*}
Mathematica [A] time = 0.010522, size = 25, normalized size = 0.47 \[ \frac{-9 x^3-38 x^2-132 x+144}{\sqrt{1-2 x}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 25, normalized size = 0.5 \begin{align*} -{(9\,{x}^{3}+38\,{x}^{2}+132\,x-144){\frac{1}{\sqrt{1-2\,x}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.05032, size = 50, normalized size = 0.94 \begin{align*} \frac{9}{8} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{103}{8} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{707}{8} \, \sqrt{-2 \, x + 1} + \frac{539}{8 \, \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.63808, size = 77, normalized size = 1.45 \begin{align*} \frac{{\left (9 \, x^{3} + 38 \, x^{2} + 132 \, x - 144\right )} \sqrt{-2 \, x + 1}}{2 \, x - 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 11.5917, size = 46, normalized size = 0.87 \begin{align*} \frac{9 \left (1 - 2 x\right )^{\frac{5}{2}}}{8} - \frac{103 \left (1 - 2 x\right )^{\frac{3}{2}}}{8} + \frac{707 \sqrt{1 - 2 x}}{8} + \frac{539}{8 \sqrt{1 - 2 x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.70408, size = 59, normalized size = 1.11 \begin{align*} \frac{9}{8} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{103}{8} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{707}{8} \, \sqrt{-2 \, x + 1} + \frac{539}{8 \, \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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