Optimal. Leaf size=118 \[ -\frac{729}{256} (1-2 x)^{15/2}+\frac{101331 (1-2 x)^{13/2}}{1664}-\frac{821583 (1-2 x)^{11/2}}{1408}+\frac{422919}{128} (1-2 x)^{9/2}-\frac{787185}{64} (1-2 x)^{7/2}+\frac{4084101}{128} (1-2 x)^{5/2}-\frac{7882483}{128} (1-2 x)^{3/2}+\frac{15647317}{128} \sqrt{1-2 x}+\frac{9058973}{256 \sqrt{1-2 x}} \]
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Rubi [A] time = 0.0199785, antiderivative size = 118, 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} \[ -\frac{729}{256} (1-2 x)^{15/2}+\frac{101331 (1-2 x)^{13/2}}{1664}-\frac{821583 (1-2 x)^{11/2}}{1408}+\frac{422919}{128} (1-2 x)^{9/2}-\frac{787185}{64} (1-2 x)^{7/2}+\frac{4084101}{128} (1-2 x)^{5/2}-\frac{7882483}{128} (1-2 x)^{3/2}+\frac{15647317}{128} \sqrt{1-2 x}+\frac{9058973}{256 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x)^7 (3+5 x)}{(1-2 x)^{3/2}} \, dx &=\int \left (\frac{9058973}{256 (1-2 x)^{3/2}}-\frac{15647317}{128 \sqrt{1-2 x}}+\frac{23647449}{128} \sqrt{1-2 x}-\frac{20420505}{128} (1-2 x)^{3/2}+\frac{5510295}{64} (1-2 x)^{5/2}-\frac{3806271}{128} (1-2 x)^{7/2}+\frac{821583}{128} (1-2 x)^{9/2}-\frac{101331}{128} (1-2 x)^{11/2}+\frac{10935}{256} (1-2 x)^{13/2}\right ) \, dx\\ &=\frac{9058973}{256 \sqrt{1-2 x}}+\frac{15647317}{128} \sqrt{1-2 x}-\frac{7882483}{128} (1-2 x)^{3/2}+\frac{4084101}{128} (1-2 x)^{5/2}-\frac{787185}{64} (1-2 x)^{7/2}+\frac{422919}{128} (1-2 x)^{9/2}-\frac{821583 (1-2 x)^{11/2}}{1408}+\frac{101331 (1-2 x)^{13/2}}{1664}-\frac{729}{256} (1-2 x)^{15/2}\\ \end{align*}
Mathematica [A] time = 0.0225349, size = 53, normalized size = 0.45 \[ \frac{-104247 x^8-697653 x^7-2168775 x^6-4220622 x^5-5949090 x^4-6921432 x^3-8106616 x^2-16881328 x+16936240}{143 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 50, normalized size = 0.4 \begin{align*} -{\frac{104247\,{x}^{8}+697653\,{x}^{7}+2168775\,{x}^{6}+4220622\,{x}^{5}+5949090\,{x}^{4}+6921432\,{x}^{3}+8106616\,{x}^{2}+16881328\,x-16936240}{143}{\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 = 2.29659, size = 111, normalized size = 0.94 \begin{align*} -\frac{729}{256} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} + \frac{101331}{1664} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{821583}{1408} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{422919}{128} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{787185}{64} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{4084101}{128} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{7882483}{128} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{15647317}{128} \, \sqrt{-2 \, x + 1} + \frac{9058973}{256 \, \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.57449, size = 205, normalized size = 1.74 \begin{align*} \frac{{\left (104247 \, x^{8} + 697653 \, x^{7} + 2168775 \, x^{6} + 4220622 \, x^{5} + 5949090 \, x^{4} + 6921432 \, x^{3} + 8106616 \, x^{2} + 16881328 \, x - 16936240\right )} \sqrt{-2 \, x + 1}}{143 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 44.1016, size = 105, normalized size = 0.89 \begin{align*} - \frac{729 \left (1 - 2 x\right )^{\frac{15}{2}}}{256} + \frac{101331 \left (1 - 2 x\right )^{\frac{13}{2}}}{1664} - \frac{821583 \left (1 - 2 x\right )^{\frac{11}{2}}}{1408} + \frac{422919 \left (1 - 2 x\right )^{\frac{9}{2}}}{128} - \frac{787185 \left (1 - 2 x\right )^{\frac{7}{2}}}{64} + \frac{4084101 \left (1 - 2 x\right )^{\frac{5}{2}}}{128} - \frac{7882483 \left (1 - 2 x\right )^{\frac{3}{2}}}{128} + \frac{15647317 \sqrt{1 - 2 x}}{128} + \frac{9058973}{256 \sqrt{1 - 2 x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.01637, size = 167, normalized size = 1.42 \begin{align*} \frac{729}{256} \,{\left (2 \, x - 1\right )}^{7} \sqrt{-2 \, x + 1} + \frac{101331}{1664} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} + \frac{821583}{1408} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{422919}{128} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{787185}{64} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{4084101}{128} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{7882483}{128} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{15647317}{128} \, \sqrt{-2 \, x + 1} + \frac{9058973}{256 \, \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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