Optimal. Leaf size=53 \[ \frac{75}{104} (1-2 x)^{13/2}-\frac{505}{88} (1-2 x)^{11/2}+\frac{1133}{72} (1-2 x)^{9/2}-\frac{121}{8} (1-2 x)^{7/2} \]
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Rubi [A] time = 0.0106357, antiderivative size = 53, 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} \[ \frac{75}{104} (1-2 x)^{13/2}-\frac{505}{88} (1-2 x)^{11/2}+\frac{1133}{72} (1-2 x)^{9/2}-\frac{121}{8} (1-2 x)^{7/2} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x)^{5/2} (2+3 x) (3+5 x)^2 \, dx &=\int \left (\frac{847}{8} (1-2 x)^{5/2}-\frac{1133}{8} (1-2 x)^{7/2}+\frac{505}{8} (1-2 x)^{9/2}-\frac{75}{8} (1-2 x)^{11/2}\right ) \, dx\\ &=-\frac{121}{8} (1-2 x)^{7/2}+\frac{1133}{72} (1-2 x)^{9/2}-\frac{505}{88} (1-2 x)^{11/2}+\frac{75}{104} (1-2 x)^{13/2}\\ \end{align*}
Mathematica [A] time = 0.0135188, size = 28, normalized size = 0.53 \[ -\frac{(1-2 x)^{7/2} \left (7425 x^3+18405 x^2+16531 x+5671\right )}{1287} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 25, normalized size = 0.5 \begin{align*} -{\frac{7425\,{x}^{3}+18405\,{x}^{2}+16531\,x+5671}{1287} \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 = 1.36408, size = 50, normalized size = 0.94 \begin{align*} \frac{75}{104} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{505}{88} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{1133}{72} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{121}{8} \,{\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 = 1.48552, size = 135, normalized size = 2.55 \begin{align*} \frac{1}{1287} \,{\left (59400 \, x^{6} + 58140 \, x^{5} - 44062 \, x^{4} - 49999 \, x^{3} + 12729 \, x^{2} + 17495 \, x - 5671\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.93246, size = 100, normalized size = 1.89 \begin{align*} \frac{600 x^{6} \sqrt{1 - 2 x}}{13} + \frac{6460 x^{5} \sqrt{1 - 2 x}}{143} - \frac{44062 x^{4} \sqrt{1 - 2 x}}{1287} - \frac{49999 x^{3} \sqrt{1 - 2 x}}{1287} + \frac{4243 x^{2} \sqrt{1 - 2 x}}{429} + \frac{17495 x \sqrt{1 - 2 x}}{1287} - \frac{5671 \sqrt{1 - 2 x}}{1287} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.0376, size = 88, normalized size = 1.66 \begin{align*} \frac{75}{104} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} + \frac{505}{88} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{1133}{72} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{121}{8} \,{\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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