Optimal. Leaf size=92 \[ -\frac{3375}{704} (1-2 x)^{11/2}+\frac{1275}{16} (1-2 x)^{9/2}-\frac{260055}{448} (1-2 x)^{7/2}+\frac{98209}{40} (1-2 x)^{5/2}-\frac{444983}{64} (1-2 x)^{3/2}+\frac{302379}{16} \sqrt{1-2 x}+\frac{456533}{64 \sqrt{1-2 x}} \]
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Rubi [A] time = 0.0192098, antiderivative size = 92, 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} \[ -\frac{3375}{704} (1-2 x)^{11/2}+\frac{1275}{16} (1-2 x)^{9/2}-\frac{260055}{448} (1-2 x)^{7/2}+\frac{98209}{40} (1-2 x)^{5/2}-\frac{444983}{64} (1-2 x)^{3/2}+\frac{302379}{16} \sqrt{1-2 x}+\frac{456533}{64 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^3 (3+5 x)^3}{(1-2 x)^{3/2}} \, dx &=\int \left (\frac{456533}{64 (1-2 x)^{3/2}}-\frac{302379}{16 \sqrt{1-2 x}}+\frac{1334949}{64} \sqrt{1-2 x}-\frac{98209}{8} (1-2 x)^{3/2}+\frac{260055}{64} (1-2 x)^{5/2}-\frac{11475}{16} (1-2 x)^{7/2}+\frac{3375}{64} (1-2 x)^{9/2}\right ) \, dx\\ &=\frac{456533}{64 \sqrt{1-2 x}}+\frac{302379}{16} \sqrt{1-2 x}-\frac{444983}{64} (1-2 x)^{3/2}+\frac{98209}{40} (1-2 x)^{5/2}-\frac{260055}{448} (1-2 x)^{7/2}+\frac{1275}{16} (1-2 x)^{9/2}-\frac{3375}{704} (1-2 x)^{11/2}\\ \end{align*}
Mathematica [A] time = 0.0188514, size = 43, normalized size = 0.47 \[ \frac{-118125 x^6-627375 x^5-1564350 x^4-2569643 x^3-3611453 x^2-8012926 x+8096086}{385 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 40, normalized size = 0.4 \begin{align*} -{\frac{118125\,{x}^{6}+627375\,{x}^{5}+1564350\,{x}^{4}+2569643\,{x}^{3}+3611453\,{x}^{2}+8012926\,x-8096086}{385}{\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 = 2.5011, size = 86, normalized size = 0.93 \begin{align*} -\frac{3375}{704} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{1275}{16} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{260055}{448} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{98209}{40} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{444983}{64} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{302379}{16} \, \sqrt{-2 \, x + 1} + \frac{456533}{64 \, \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.52041, size = 165, normalized size = 1.79 \begin{align*} \frac{{\left (118125 \, x^{6} + 627375 \, x^{5} + 1564350 \, x^{4} + 2569643 \, x^{3} + 3611453 \, x^{2} + 8012926 \, x - 8096086\right )} \sqrt{-2 \, x + 1}}{385 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 28.8409, size = 82, normalized size = 0.89 \begin{align*} - \frac{3375 \left (1 - 2 x\right )^{\frac{11}{2}}}{704} + \frac{1275 \left (1 - 2 x\right )^{\frac{9}{2}}}{16} - \frac{260055 \left (1 - 2 x\right )^{\frac{7}{2}}}{448} + \frac{98209 \left (1 - 2 x\right )^{\frac{5}{2}}}{40} - \frac{444983 \left (1 - 2 x\right )^{\frac{3}{2}}}{64} + \frac{302379 \sqrt{1 - 2 x}}{16} + \frac{456533}{64 \sqrt{1 - 2 x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.94652, size = 124, normalized size = 1.35 \begin{align*} \frac{3375}{704} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{1275}{16} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{260055}{448} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{98209}{40} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{444983}{64} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{302379}{16} \, \sqrt{-2 \, x + 1} + \frac{456533}{64 \, \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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