Optimal. Leaf size=66 \[ -\frac{25}{16} (1-2 x)^{15/2}+\frac{1675}{104} (1-2 x)^{13/2}-\frac{255}{4} (1-2 x)^{11/2}+\frac{2783}{24} (1-2 x)^{9/2}-\frac{1331}{16} (1-2 x)^{7/2} \]
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Rubi [A] time = 0.0119495, 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} \[ -\frac{25}{16} (1-2 x)^{15/2}+\frac{1675}{104} (1-2 x)^{13/2}-\frac{255}{4} (1-2 x)^{11/2}+\frac{2783}{24} (1-2 x)^{9/2}-\frac{1331}{16} (1-2 x)^{7/2} \]
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)^3 \, dx &=\int \left (\frac{9317}{16} (1-2 x)^{5/2}-\frac{8349}{8} (1-2 x)^{7/2}+\frac{2805}{4} (1-2 x)^{9/2}-\frac{1675}{8} (1-2 x)^{11/2}+\frac{375}{16} (1-2 x)^{13/2}\right ) \, dx\\ &=-\frac{1331}{16} (1-2 x)^{7/2}+\frac{2783}{24} (1-2 x)^{9/2}-\frac{255}{4} (1-2 x)^{11/2}+\frac{1675}{104} (1-2 x)^{13/2}-\frac{25}{16} (1-2 x)^{15/2}\\ \end{align*}
Mathematica [A] time = 0.0154722, size = 33, normalized size = 0.5 \[ -\frac{1}{39} (1-2 x)^{7/2} \left (975 x^4+3075 x^3+3870 x^2+2381 x+641\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 30, normalized size = 0.5 \begin{align*} -{\frac{975\,{x}^{4}+3075\,{x}^{3}+3870\,{x}^{2}+2381\,x+641}{39} \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 = 2.88065, size = 62, normalized size = 0.94 \begin{align*} -\frac{25}{16} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} + \frac{1675}{104} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{255}{4} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{2783}{24} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{1331}{16} \,{\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 = 1.31275, size = 136, normalized size = 2.06 \begin{align*} \frac{1}{39} \,{\left (7800 \, x^{7} + 12900 \, x^{6} - 90 \, x^{5} - 9917 \, x^{4} - 3299 \, x^{3} + 2724 \, x^{2} + 1465 \, x - 641\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 13.1815, size = 58, normalized size = 0.88 \begin{align*} - \frac{25 \left (1 - 2 x\right )^{\frac{15}{2}}}{16} + \frac{1675 \left (1 - 2 x\right )^{\frac{13}{2}}}{104} - \frac{255 \left (1 - 2 x\right )^{\frac{11}{2}}}{4} + \frac{2783 \left (1 - 2 x\right )^{\frac{9}{2}}}{24} - \frac{1331 \left (1 - 2 x\right )^{\frac{7}{2}}}{16} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.94232, size = 109, normalized size = 1.65 \begin{align*} \frac{25}{16} \,{\left (2 \, x - 1\right )}^{7} \sqrt{-2 \, x + 1} + \frac{1675}{104} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} + \frac{255}{4} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{2783}{24} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{1331}{16} \,{\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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