Optimal. Leaf size=79 \[ \frac{675}{544} (1-2 x)^{17/2}-\frac{513}{32} (1-2 x)^{15/2}+\frac{17541}{208} (1-2 x)^{13/2}-\frac{39977}{176} (1-2 x)^{11/2}+\frac{91091}{288} (1-2 x)^{9/2}-\frac{5929}{32} (1-2 x)^{7/2} \]
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Rubi [A] time = 0.0156546, 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} \[ \frac{675}{544} (1-2 x)^{17/2}-\frac{513}{32} (1-2 x)^{15/2}+\frac{17541}{208} (1-2 x)^{13/2}-\frac{39977}{176} (1-2 x)^{11/2}+\frac{91091}{288} (1-2 x)^{9/2}-\frac{5929}{32} (1-2 x)^{7/2} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int (1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^2 \, dx &=\int \left (\frac{41503}{32} (1-2 x)^{5/2}-\frac{91091}{32} (1-2 x)^{7/2}+\frac{39977}{16} (1-2 x)^{9/2}-\frac{17541}{16} (1-2 x)^{11/2}+\frac{7695}{32} (1-2 x)^{13/2}-\frac{675}{32} (1-2 x)^{15/2}\right ) \, dx\\ &=-\frac{5929}{32} (1-2 x)^{7/2}+\frac{91091}{288} (1-2 x)^{9/2}-\frac{39977}{176} (1-2 x)^{11/2}+\frac{17541}{208} (1-2 x)^{13/2}-\frac{513}{32} (1-2 x)^{15/2}+\frac{675}{544} (1-2 x)^{17/2}\\ \end{align*}
Mathematica [A] time = 0.0184694, size = 38, normalized size = 0.48 \[ -\frac{(1-2 x)^{7/2} \left (868725 x^5+3440151 x^4+5708637 x^3+5069475 x^2+2497634 x+581846\right )}{21879} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 35, normalized size = 0.4 \begin{align*} -{\frac{868725\,{x}^{5}+3440151\,{x}^{4}+5708637\,{x}^{3}+5069475\,{x}^{2}+2497634\,x+581846}{21879} \left ( 1-2\,x \right ) ^{{\frac{7}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 3.66137, size = 74, normalized size = 0.94 \begin{align*} \frac{675}{544} \,{\left (-2 \, x + 1\right )}^{\frac{17}{2}} - \frac{513}{32} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} + \frac{17541}{208} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{39977}{176} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{91091}{288} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{5929}{32} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.51579, size = 193, normalized size = 2.44 \begin{align*} \frac{1}{21879} \,{\left (6949800 \, x^{8} + 17096508 \, x^{7} + 9599634 \, x^{6} - 8175663 \, x^{5} - 10040957 \, x^{4} - 608627 \, x^{3} + 2934177 \, x^{2} + 993442 \, x - 581846\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 16.1773, size = 70, normalized size = 0.89 \begin{align*} \frac{675 \left (1 - 2 x\right )^{\frac{17}{2}}}{544} - \frac{513 \left (1 - 2 x\right )^{\frac{15}{2}}}{32} + \frac{17541 \left (1 - 2 x\right )^{\frac{13}{2}}}{208} - \frac{39977 \left (1 - 2 x\right )^{\frac{11}{2}}}{176} + \frac{91091 \left (1 - 2 x\right )^{\frac{9}{2}}}{288} - \frac{5929 \left (1 - 2 x\right )^{\frac{7}{2}}}{32} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.88124, size = 131, normalized size = 1.66 \begin{align*} \frac{675}{544} \,{\left (2 \, x - 1\right )}^{8} \sqrt{-2 \, x + 1} + \frac{513}{32} \,{\left (2 \, x - 1\right )}^{7} \sqrt{-2 \, x + 1} + \frac{17541}{208} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} + \frac{39977}{176} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{91091}{288} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{5929}{32} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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