Optimal. Leaf size=66 \[ -\frac{375}{208} (1-2 x)^{13/2}+\frac{1675}{88} (1-2 x)^{11/2}-\frac{935}{12} (1-2 x)^{9/2}+\frac{8349}{56} (1-2 x)^{7/2}-\frac{9317}{80} (1-2 x)^{5/2} \]
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Rubi [A] time = 0.0116072, antiderivative size = 66, 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} \[ -\frac{375}{208} (1-2 x)^{13/2}+\frac{1675}{88} (1-2 x)^{11/2}-\frac{935}{12} (1-2 x)^{9/2}+\frac{8349}{56} (1-2 x)^{7/2}-\frac{9317}{80} (1-2 x)^{5/2} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x)^{3/2} (2+3 x) (3+5 x)^3 \, dx &=\int \left (\frac{9317}{16} (1-2 x)^{3/2}-\frac{8349}{8} (1-2 x)^{5/2}+\frac{2805}{4} (1-2 x)^{7/2}-\frac{1675}{8} (1-2 x)^{9/2}+\frac{375}{16} (1-2 x)^{11/2}\right ) \, dx\\ &=-\frac{9317}{80} (1-2 x)^{5/2}+\frac{8349}{56} (1-2 x)^{7/2}-\frac{935}{12} (1-2 x)^{9/2}+\frac{1675}{88} (1-2 x)^{11/2}-\frac{375}{208} (1-2 x)^{13/2}\\ \end{align*}
Mathematica [A] time = 0.0151345, size = 33, normalized size = 0.5 \[ -\frac{(1-2 x)^{5/2} \left (433125 x^4+1420125 x^3+1899800 x^2+1295695 x+421301\right )}{15015} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 30, normalized size = 0.5 \begin{align*} -{\frac{433125\,{x}^{4}+1420125\,{x}^{3}+1899800\,{x}^{2}+1295695\,x+421301}{15015} \left ( 1-2\,x \right ) ^{{\frac{5}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.16934, size = 62, normalized size = 0.94 \begin{align*} -\frac{375}{208} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} + \frac{1675}{88} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - \frac{935}{12} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{8349}{56} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{9317}{80} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.17222, size = 154, normalized size = 2.33 \begin{align*} -\frac{1}{15015} \,{\left (1732500 \, x^{6} + 3948000 \, x^{5} + 2351825 \, x^{4} - 996295 \, x^{3} - 1597776 \, x^{2} - 389509 \, x + 421301\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 10.0382, size = 58, normalized size = 0.88 \begin{align*} - \frac{375 \left (1 - 2 x\right )^{\frac{13}{2}}}{208} + \frac{1675 \left (1 - 2 x\right )^{\frac{11}{2}}}{88} - \frac{935 \left (1 - 2 x\right )^{\frac{9}{2}}}{12} + \frac{8349 \left (1 - 2 x\right )^{\frac{7}{2}}}{56} - \frac{9317 \left (1 - 2 x\right )^{\frac{5}{2}}}{80} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.81257, size = 109, normalized size = 1.65 \begin{align*} -\frac{375}{208} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} - \frac{1675}{88} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} - \frac{935}{12} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{8349}{56} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{9317}{80} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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