Optimal. Leaf size=79 \[ \frac{1125}{416} (1-2 x)^{13/2}-\frac{12675}{352} (1-2 x)^{11/2}+\frac{28555}{144} (1-2 x)^{9/2}-\frac{64317}{112} (1-2 x)^{7/2}+\frac{144837}{160} (1-2 x)^{5/2}-\frac{65219}{96} (1-2 x)^{3/2} \]
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Rubi [A] time = 0.0142067, 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} \[ \frac{1125}{416} (1-2 x)^{13/2}-\frac{12675}{352} (1-2 x)^{11/2}+\frac{28555}{144} (1-2 x)^{9/2}-\frac{64317}{112} (1-2 x)^{7/2}+\frac{144837}{160} (1-2 x)^{5/2}-\frac{65219}{96} (1-2 x)^{3/2} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \sqrt{1-2 x} (2+3 x)^2 (3+5 x)^3 \, dx &=\int \left (\frac{65219}{32} \sqrt{1-2 x}-\frac{144837}{32} (1-2 x)^{3/2}+\frac{64317}{16} (1-2 x)^{5/2}-\frac{28555}{16} (1-2 x)^{7/2}+\frac{12675}{32} (1-2 x)^{9/2}-\frac{1125}{32} (1-2 x)^{11/2}\right ) \, dx\\ &=-\frac{65219}{96} (1-2 x)^{3/2}+\frac{144837}{160} (1-2 x)^{5/2}-\frac{64317}{112} (1-2 x)^{7/2}+\frac{28555}{144} (1-2 x)^{9/2}-\frac{12675}{352} (1-2 x)^{11/2}+\frac{1125}{416} (1-2 x)^{13/2}\\ \end{align*}
Mathematica [A] time = 0.0164893, size = 38, normalized size = 0.48 \[ -\frac{(1-2 x)^{3/2} \left (3898125 x^5+16206750 x^4+29300075 x^3+30337080 x^2+19918608 x+8261156\right )}{45045} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 35, normalized size = 0.4 \begin{align*} -{\frac{3898125\,{x}^{5}+16206750\,{x}^{4}+29300075\,{x}^{3}+30337080\,{x}^{2}+19918608\,x+8261156}{45045} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.21828, size = 74, normalized size = 0.94 \begin{align*} \frac{1125}{416} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{12675}{352} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{28555}{144} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{64317}{112} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{144837}{160} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{65219}{96} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.50751, size = 161, normalized size = 2.04 \begin{align*} \frac{1}{45045} \,{\left (7796250 \, x^{6} + 28515375 \, x^{5} + 42393400 \, x^{4} + 31374085 \, x^{3} + 9500136 \, x^{2} - 3396296 \, x - 8261156\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.11144, size = 70, normalized size = 0.89 \begin{align*} \frac{1125 \left (1 - 2 x\right )^{\frac{13}{2}}}{416} - \frac{12675 \left (1 - 2 x\right )^{\frac{11}{2}}}{352} + \frac{28555 \left (1 - 2 x\right )^{\frac{9}{2}}}{144} - \frac{64317 \left (1 - 2 x\right )^{\frac{7}{2}}}{112} + \frac{144837 \left (1 - 2 x\right )^{\frac{5}{2}}}{160} - \frac{65219 \left (1 - 2 x\right )^{\frac{3}{2}}}{96} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.17635, size = 122, normalized size = 1.54 \begin{align*} \frac{1125}{416} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} + \frac{12675}{352} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{28555}{144} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{64317}{112} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{144837}{160} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{65219}{96} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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