Optimal. Leaf size=79 \[ \frac{75}{32} (1-2 x)^{15/2}-\frac{975}{32} (1-2 x)^{13/2}+\frac{28555}{176} (1-2 x)^{11/2}-\frac{21439}{48} (1-2 x)^{9/2}+\frac{20691}{32} (1-2 x)^{7/2}-\frac{65219}{160} (1-2 x)^{5/2} \]
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Rubi [A] time = 0.0153488, 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} \[ \frac{75}{32} (1-2 x)^{15/2}-\frac{975}{32} (1-2 x)^{13/2}+\frac{28555}{176} (1-2 x)^{11/2}-\frac{21439}{48} (1-2 x)^{9/2}+\frac{20691}{32} (1-2 x)^{7/2}-\frac{65219}{160} (1-2 x)^{5/2} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^3 \, dx &=\int \left (\frac{65219}{32} (1-2 x)^{3/2}-\frac{144837}{32} (1-2 x)^{5/2}+\frac{64317}{16} (1-2 x)^{7/2}-\frac{28555}{16} (1-2 x)^{9/2}+\frac{12675}{32} (1-2 x)^{11/2}-\frac{1125}{32} (1-2 x)^{13/2}\right ) \, dx\\ &=-\frac{65219}{160} (1-2 x)^{5/2}+\frac{20691}{32} (1-2 x)^{7/2}-\frac{21439}{48} (1-2 x)^{9/2}+\frac{28555}{176} (1-2 x)^{11/2}-\frac{975}{32} (1-2 x)^{13/2}+\frac{75}{32} (1-2 x)^{15/2}\\ \end{align*}
Mathematica [A] time = 0.0176951, size = 38, normalized size = 0.48 \[ -\frac{1}{165} (1-2 x)^{5/2} \left (12375 x^5+49500 x^4+84225 x^3+78730 x^2+42860 x+12136\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 35, normalized size = 0.4 \begin{align*} -{\frac{12375\,{x}^{5}+49500\,{x}^{4}+84225\,{x}^{3}+78730\,{x}^{2}+42860\,x+12136}{165} \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 = 1.25238, size = 74, normalized size = 0.94 \begin{align*} \frac{75}{32} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} - \frac{975}{32} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} + \frac{28555}{176} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - \frac{21439}{48} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{20691}{32} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{65219}{160} \,{\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 = 1.38783, size = 154, normalized size = 1.95 \begin{align*} -\frac{1}{165} \,{\left (49500 \, x^{7} + 148500 \, x^{6} + 151275 \, x^{5} + 27520 \, x^{4} - 59255 \, x^{3} - 44166 \, x^{2} - 5684 \, x + 12136\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 12.8094, size = 70, normalized size = 0.89 \begin{align*} \frac{75 \left (1 - 2 x\right )^{\frac{15}{2}}}{32} - \frac{975 \left (1 - 2 x\right )^{\frac{13}{2}}}{32} + \frac{28555 \left (1 - 2 x\right )^{\frac{11}{2}}}{176} - \frac{21439 \left (1 - 2 x\right )^{\frac{9}{2}}}{48} + \frac{20691 \left (1 - 2 x\right )^{\frac{7}{2}}}{32} - \frac{65219 \left (1 - 2 x\right )^{\frac{5}{2}}}{160} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.80198, size = 131, normalized size = 1.66 \begin{align*} -\frac{75}{32} \,{\left (2 \, x - 1\right )}^{7} \sqrt{-2 \, x + 1} - \frac{975}{32} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} - \frac{28555}{176} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} - \frac{21439}{48} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{20691}{32} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{65219}{160} \,{\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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