Optimal. Leaf size=79 \[ \frac{125}{32} (1-2 x)^{9/2}-\frac{12675}{224} (1-2 x)^{7/2}+\frac{5711}{16} (1-2 x)^{5/2}-\frac{21439}{16} (1-2 x)^{3/2}+\frac{144837}{32} \sqrt{1-2 x}+\frac{65219}{32 \sqrt{1-2 x}} \]
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Rubi [A] time = 0.0161979, antiderivative size = 79, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042, Rules used = {88} \[ \frac{125}{32} (1-2 x)^{9/2}-\frac{12675}{224} (1-2 x)^{7/2}+\frac{5711}{16} (1-2 x)^{5/2}-\frac{21439}{16} (1-2 x)^{3/2}+\frac{144837}{32} \sqrt{1-2 x}+\frac{65219}{32 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^2 (3+5 x)^3}{(1-2 x)^{3/2}} \, dx &=\int \left (\frac{65219}{32 (1-2 x)^{3/2}}-\frac{144837}{32 \sqrt{1-2 x}}+\frac{64317}{16} \sqrt{1-2 x}-\frac{28555}{16} (1-2 x)^{3/2}+\frac{12675}{32} (1-2 x)^{5/2}-\frac{1125}{32} (1-2 x)^{7/2}\right ) \, dx\\ &=\frac{65219}{32 \sqrt{1-2 x}}+\frac{144837}{32} \sqrt{1-2 x}-\frac{21439}{16} (1-2 x)^{3/2}+\frac{5711}{16} (1-2 x)^{5/2}-\frac{12675}{224} (1-2 x)^{7/2}+\frac{125}{32} (1-2 x)^{9/2}\\ \end{align*}
Mathematica [A] time = 0.0159379, size = 38, normalized size = 0.48 \[ \frac{-875 x^5-4150 x^4-9501 x^3-15948 x^2-37944 x+38700}{7 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 35, normalized size = 0.4 \begin{align*} -{\frac{875\,{x}^{5}+4150\,{x}^{4}+9501\,{x}^{3}+15948\,{x}^{2}+37944\,x-38700}{7}{\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 = 1.05822, size = 74, normalized size = 0.94 \begin{align*} \frac{125}{32} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{12675}{224} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{5711}{16} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{21439}{16} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{144837}{32} \, \sqrt{-2 \, x + 1} + \frac{65219}{32 \, \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.58219, size = 124, normalized size = 1.57 \begin{align*} \frac{{\left (875 \, x^{5} + 4150 \, x^{4} + 9501 \, x^{3} + 15948 \, x^{2} + 37944 \, x - 38700\right )} \sqrt{-2 \, x + 1}}{7 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 22.1413, size = 70, normalized size = 0.89 \begin{align*} \frac{125 \left (1 - 2 x\right )^{\frac{9}{2}}}{32} - \frac{12675 \left (1 - 2 x\right )^{\frac{7}{2}}}{224} + \frac{5711 \left (1 - 2 x\right )^{\frac{5}{2}}}{16} - \frac{21439 \left (1 - 2 x\right )^{\frac{3}{2}}}{16} + \frac{144837 \sqrt{1 - 2 x}}{32} + \frac{65219}{32 \sqrt{1 - 2 x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.41436, size = 103, normalized size = 1.3 \begin{align*} \frac{125}{32} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{12675}{224} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{5711}{16} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{21439}{16} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{144837}{32} \, \sqrt{-2 \, x + 1} + \frac{65219}{32 \, \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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