Optimal. Leaf size=79 \[ \frac{675}{224} (1-2 x)^{7/2}-\frac{1539}{32} (1-2 x)^{5/2}+\frac{5847}{16} (1-2 x)^{3/2}-\frac{39977}{16} \sqrt{1-2 x}-\frac{91091}{32 \sqrt{1-2 x}}+\frac{41503}{96 (1-2 x)^{3/2}} \]
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Rubi [A] time = 0.0153137, 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} \[ \frac{675}{224} (1-2 x)^{7/2}-\frac{1539}{32} (1-2 x)^{5/2}+\frac{5847}{16} (1-2 x)^{3/2}-\frac{39977}{16} \sqrt{1-2 x}-\frac{91091}{32 \sqrt{1-2 x}}+\frac{41503}{96 (1-2 x)^{3/2}} \]
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)^{5/2}} \, dx &=\int \left (\frac{41503}{32 (1-2 x)^{5/2}}-\frac{91091}{32 (1-2 x)^{3/2}}+\frac{39977}{16 \sqrt{1-2 x}}-\frac{17541}{16} \sqrt{1-2 x}+\frac{7695}{32} (1-2 x)^{3/2}-\frac{675}{32} (1-2 x)^{5/2}\right ) \, dx\\ &=\frac{41503}{96 (1-2 x)^{3/2}}-\frac{91091}{32 \sqrt{1-2 x}}-\frac{39977}{16} \sqrt{1-2 x}+\frac{5847}{16} (1-2 x)^{3/2}-\frac{1539}{32} (1-2 x)^{5/2}+\frac{675}{224} (1-2 x)^{7/2}\\ \end{align*}
Mathematica [A] time = 0.0147079, size = 38, normalized size = 0.48 \[ -\frac{2025 x^5+11097 x^4+34137 x^3+139497 x^2-290838 x+96442}{21 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 35, normalized size = 0.4 \begin{align*} -{\frac{2025\,{x}^{5}+11097\,{x}^{4}+34137\,{x}^{3}+139497\,{x}^{2}-290838\,x+96442}{21} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0491, size = 69, normalized size = 0.87 \begin{align*} \frac{675}{224} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{1539}{32} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{5847}{16} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{39977}{16} \, \sqrt{-2 \, x + 1} + \frac{539 \,{\left (507 \, x - 215\right )}}{48 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.58872, size = 144, normalized size = 1.82 \begin{align*} -\frac{{\left (2025 \, x^{5} + 11097 \, x^{4} + 34137 \, x^{3} + 139497 \, x^{2} - 290838 \, x + 96442\right )} \sqrt{-2 \, x + 1}}{21 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 19.8033, size = 70, normalized size = 0.89 \begin{align*} \frac{675 \left (1 - 2 x\right )^{\frac{7}{2}}}{224} - \frac{1539 \left (1 - 2 x\right )^{\frac{5}{2}}}{32} + \frac{5847 \left (1 - 2 x\right )^{\frac{3}{2}}}{16} - \frac{39977 \sqrt{1 - 2 x}}{16} - \frac{91091}{32 \sqrt{1 - 2 x}} + \frac{41503}{96 \left (1 - 2 x\right )^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.52176, size = 97, normalized size = 1.23 \begin{align*} -\frac{675}{224} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{1539}{32} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{5847}{16} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{39977}{16} \, \sqrt{-2 \, x + 1} - \frac{539 \,{\left (507 \, x - 215\right )}}{48 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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