Optimal. Leaf size=79 \[ \frac{1125}{544} (1-2 x)^{17/2}-\frac{845}{32} (1-2 x)^{15/2}+\frac{28555}{208} (1-2 x)^{13/2}-\frac{5847}{16} (1-2 x)^{11/2}+\frac{16093}{32} (1-2 x)^{9/2}-\frac{9317}{32} (1-2 x)^{7/2} \]
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Rubi [A] time = 0.0158904, 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} \[ \frac{1125}{544} (1-2 x)^{17/2}-\frac{845}{32} (1-2 x)^{15/2}+\frac{28555}{208} (1-2 x)^{13/2}-\frac{5847}{16} (1-2 x)^{11/2}+\frac{16093}{32} (1-2 x)^{9/2}-\frac{9317}{32} (1-2 x)^{7/2} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int (1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^3 \, dx &=\int \left (\frac{65219}{32} (1-2 x)^{5/2}-\frac{144837}{32} (1-2 x)^{7/2}+\frac{64317}{16} (1-2 x)^{9/2}-\frac{28555}{16} (1-2 x)^{11/2}+\frac{12675}{32} (1-2 x)^{13/2}-\frac{1125}{32} (1-2 x)^{15/2}\right ) \, dx\\ &=-\frac{9317}{32} (1-2 x)^{7/2}+\frac{16093}{32} (1-2 x)^{9/2}-\frac{5847}{16} (1-2 x)^{11/2}+\frac{28555}{208} (1-2 x)^{13/2}-\frac{845}{32} (1-2 x)^{15/2}+\frac{1125}{544} (1-2 x)^{17/2}\\ \end{align*}
Mathematica [A] time = 0.0189067, size = 38, normalized size = 0.48 \[ -\frac{1}{221} (1-2 x)^{7/2} \left (14625 x^5+56810 x^4+92535 x^3+80748 x^2+39160 x+9004\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 35, normalized size = 0.4 \begin{align*} -{\frac{14625\,{x}^{5}+56810\,{x}^{4}+92535\,{x}^{3}+80748\,{x}^{2}+39160\,x+9004}{221} \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 = 3.33019, size = 74, normalized size = 0.94 \begin{align*} \frac{1125}{544} \,{\left (-2 \, x + 1\right )}^{\frac{17}{2}} - \frac{845}{32} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} + \frac{28555}{208} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{5847}{16} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{16093}{32} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{9317}{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 = 1.34214, size = 171, normalized size = 2.16 \begin{align*} \frac{1}{221} \,{\left (117000 \, x^{8} + 278980 \, x^{7} + 146310 \, x^{6} - 138201 \, x^{5} - 157296 \, x^{4} - 5935 \, x^{3} + 46164 \, x^{2} + 14864 \, x - 9004\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 16.1935, size = 70, normalized size = 0.89 \begin{align*} \frac{1125 \left (1 - 2 x\right )^{\frac{17}{2}}}{544} - \frac{845 \left (1 - 2 x\right )^{\frac{15}{2}}}{32} + \frac{28555 \left (1 - 2 x\right )^{\frac{13}{2}}}{208} - \frac{5847 \left (1 - 2 x\right )^{\frac{11}{2}}}{16} + \frac{16093 \left (1 - 2 x\right )^{\frac{9}{2}}}{32} - \frac{9317 \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 = 2.73069, size = 131, normalized size = 1.66 \begin{align*} \frac{1125}{544} \,{\left (2 \, x - 1\right )}^{8} \sqrt{-2 \, x + 1} + \frac{845}{32} \,{\left (2 \, x - 1\right )}^{7} \sqrt{-2 \, x + 1} + \frac{28555}{208} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} + \frac{5847}{16} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{16093}{32} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{9317}{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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