Optimal. Leaf size=79 \[ \frac{75}{32} (1-2 x)^{9/2}-\frac{7695}{224} (1-2 x)^{7/2}+\frac{17541}{80} (1-2 x)^{5/2}-\frac{39977}{48} (1-2 x)^{3/2}+\frac{91091}{32} \sqrt{1-2 x}+\frac{41503}{32 \sqrt{1-2 x}} \]
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Rubi [A] time = 0.0153282, 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} \[ \frac{75}{32} (1-2 x)^{9/2}-\frac{7695}{224} (1-2 x)^{7/2}+\frac{17541}{80} (1-2 x)^{5/2}-\frac{39977}{48} (1-2 x)^{3/2}+\frac{91091}{32} \sqrt{1-2 x}+\frac{41503}{32 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^3 (3+5 x)^2}{(1-2 x)^{3/2}} \, dx &=\int \left (\frac{41503}{32 (1-2 x)^{3/2}}-\frac{91091}{32 \sqrt{1-2 x}}+\frac{39977}{16} \sqrt{1-2 x}-\frac{17541}{16} (1-2 x)^{3/2}+\frac{7695}{32} (1-2 x)^{5/2}-\frac{675}{32} (1-2 x)^{7/2}\right ) \, dx\\ &=\frac{41503}{32 \sqrt{1-2 x}}+\frac{91091}{32} \sqrt{1-2 x}-\frac{39977}{48} (1-2 x)^{3/2}+\frac{17541}{80} (1-2 x)^{5/2}-\frac{7695}{224} (1-2 x)^{7/2}+\frac{75}{32} (1-2 x)^{9/2}\\ \end{align*}
Mathematica [A] time = 0.0160771, size = 38, normalized size = 0.48 \[ \frac{-7875 x^5-38025 x^4-88443 x^3-150253 x^2-359726 x+367286}{105 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 35, normalized size = 0.4 \begin{align*} -{\frac{7875\,{x}^{5}+38025\,{x}^{4}+88443\,{x}^{3}+150253\,{x}^{2}+359726\,x-367286}{105}{\frac{1}{\sqrt{1-2\,x}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.99201, size = 74, normalized size = 0.94 \begin{align*} \frac{75}{32} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{7695}{224} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{17541}{80} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{39977}{48} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{91091}{32} \, \sqrt{-2 \, x + 1} + \frac{41503}{32 \, \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.50467, size = 135, normalized size = 1.71 \begin{align*} \frac{{\left (7875 \, x^{5} + 38025 \, x^{4} + 88443 \, x^{3} + 150253 \, x^{2} + 359726 \, x - 367286\right )} \sqrt{-2 \, x + 1}}{105 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 21.8675, size = 70, normalized size = 0.89 \begin{align*} \frac{75 \left (1 - 2 x\right )^{\frac{9}{2}}}{32} - \frac{7695 \left (1 - 2 x\right )^{\frac{7}{2}}}{224} + \frac{17541 \left (1 - 2 x\right )^{\frac{5}{2}}}{80} - \frac{39977 \left (1 - 2 x\right )^{\frac{3}{2}}}{48} + \frac{91091 \sqrt{1 - 2 x}}{32} + \frac{41503}{32 \sqrt{1 - 2 x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.02404, size = 103, normalized size = 1.3 \begin{align*} \frac{75}{32} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{7695}{224} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{17541}{80} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{39977}{48} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{91091}{32} \, \sqrt{-2 \, x + 1} + \frac{41503}{32 \, \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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