Optimal. Leaf size=79 \[ \frac{675}{352} (1-2 x)^{11/2}-\frac{855}{32} (1-2 x)^{9/2}+\frac{17541}{112} (1-2 x)^{7/2}-\frac{39977}{80} (1-2 x)^{5/2}+\frac{91091}{96} (1-2 x)^{3/2}-\frac{41503}{32} \sqrt{1-2 x} \]
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Rubi [A] time = 0.0145525, 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} \[ \frac{675}{352} (1-2 x)^{11/2}-\frac{855}{32} (1-2 x)^{9/2}+\frac{17541}{112} (1-2 x)^{7/2}-\frac{39977}{80} (1-2 x)^{5/2}+\frac{91091}{96} (1-2 x)^{3/2}-\frac{41503}{32} \sqrt{1-2 x} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^3 (3+5 x)^2}{\sqrt{1-2 x}} \, dx &=\int \left (\frac{41503}{32 \sqrt{1-2 x}}-\frac{91091}{32} \sqrt{1-2 x}+\frac{39977}{16} (1-2 x)^{3/2}-\frac{17541}{16} (1-2 x)^{5/2}+\frac{7695}{32} (1-2 x)^{7/2}-\frac{675}{32} (1-2 x)^{9/2}\right ) \, dx\\ &=-\frac{41503}{32} \sqrt{1-2 x}+\frac{91091}{96} (1-2 x)^{3/2}-\frac{39977}{80} (1-2 x)^{5/2}+\frac{17541}{112} (1-2 x)^{7/2}-\frac{855}{32} (1-2 x)^{9/2}+\frac{675}{352} (1-2 x)^{11/2}\\ \end{align*}
Mathematica [A] time = 0.0140756, size = 38, normalized size = 0.48 \[ -\frac{\sqrt{1-2 x} \left (70875 x^5+316575 x^4+636795 x^3+790023 x^2+743822 x+826982\right )}{1155} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 35, normalized size = 0.4 \begin{align*} -{\frac{70875\,{x}^{5}+316575\,{x}^{4}+636795\,{x}^{3}+790023\,{x}^{2}+743822\,x+826982}{1155}\sqrt{1-2\,x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06339, size = 74, normalized size = 0.94 \begin{align*} \frac{675}{352} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - \frac{855}{32} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{17541}{112} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{39977}{80} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{91091}{96} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \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 = 1.32522, size = 128, normalized size = 1.62 \begin{align*} -\frac{1}{1155} \,{\left (70875 \, x^{5} + 316575 \, x^{4} + 636795 \, x^{3} + 790023 \, x^{2} + 743822 \, x + 826982\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 42.0325, size = 70, normalized size = 0.89 \begin{align*} \frac{675 \left (1 - 2 x\right )^{\frac{11}{2}}}{352} - \frac{855 \left (1 - 2 x\right )^{\frac{9}{2}}}{32} + \frac{17541 \left (1 - 2 x\right )^{\frac{7}{2}}}{112} - \frac{39977 \left (1 - 2 x\right )^{\frac{5}{2}}}{80} + \frac{91091 \left (1 - 2 x\right )^{\frac{3}{2}}}{96} - \frac{41503 \sqrt{1 - 2 x}}{32} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.70734, size = 112, normalized size = 1.42 \begin{align*} -\frac{675}{352} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} - \frac{855}{32} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{17541}{112} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{39977}{80} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{91091}{96} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{41503}{32} \, \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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