Optimal. Leaf size=79 \[ \frac {125}{32} (1-2 x)^{9/2}-\frac {12675}{224} (1-2 x)^{7/2}+\frac {5711}{16} (1-2 x)^{5/2}-\frac {21439}{16} (1-2 x)^{3/2}+\frac {144837}{32} \sqrt {1-2 x}+\frac {65219}{32 \sqrt {1-2 x}} \]
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Rubi [A] time = 0.02, antiderivative size = 79, normalized size of antiderivative = 1.00, 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} \[ \frac {125}{32} (1-2 x)^{9/2}-\frac {12675}{224} (1-2 x)^{7/2}+\frac {5711}{16} (1-2 x)^{5/2}-\frac {21439}{16} (1-2 x)^{3/2}+\frac {144837}{32} \sqrt {1-2 x}+\frac {65219}{32 \sqrt {1-2 x}} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^2 (3+5 x)^3}{(1-2 x)^{3/2}} \, dx &=\int \left (\frac {65219}{32 (1-2 x)^{3/2}}-\frac {144837}{32 \sqrt {1-2 x}}+\frac {64317}{16} \sqrt {1-2 x}-\frac {28555}{16} (1-2 x)^{3/2}+\frac {12675}{32} (1-2 x)^{5/2}-\frac {1125}{32} (1-2 x)^{7/2}\right ) \, dx\\ &=\frac {65219}{32 \sqrt {1-2 x}}+\frac {144837}{32} \sqrt {1-2 x}-\frac {21439}{16} (1-2 x)^{3/2}+\frac {5711}{16} (1-2 x)^{5/2}-\frac {12675}{224} (1-2 x)^{7/2}+\frac {125}{32} (1-2 x)^{9/2}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 38, normalized size = 0.48 \[ \frac {-875 x^5-4150 x^4-9501 x^3-15948 x^2-37944 x+38700}{7 \sqrt {1-2 x}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.75, size = 41, normalized size = 0.52 \[ \frac {{\left (875 \, x^{5} + 4150 \, x^{4} + 9501 \, x^{3} + 15948 \, x^{2} + 37944 \, x - 38700\right )} \sqrt {-2 \, x + 1}}{7 \, {\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.26, size = 76, normalized size = 0.96 \[ \frac {125}{32} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {12675}{224} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} + \frac {5711}{16} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} - \frac {21439}{16} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + \frac {144837}{32} \, \sqrt {-2 \, x + 1} + \frac {65219}{32 \, \sqrt {-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 35, normalized size = 0.44 \[ -\frac {875 x^{5}+4150 x^{4}+9501 x^{3}+15948 x^{2}+37944 x -38700}{7 \sqrt {-2 x +1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 55, normalized size = 0.70 \[ \frac {125}{32} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {12675}{224} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} + \frac {5711}{16} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - \frac {21439}{16} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + \frac {144837}{32} \, \sqrt {-2 \, x + 1} + \frac {65219}{32 \, \sqrt {-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 55, normalized size = 0.70 \[ \frac {65219}{32\,\sqrt {1-2\,x}}+\frac {144837\,\sqrt {1-2\,x}}{32}-\frac {21439\,{\left (1-2\,x\right )}^{3/2}}{16}+\frac {5711\,{\left (1-2\,x\right )}^{5/2}}{16}-\frac {12675\,{\left (1-2\,x\right )}^{7/2}}{224}+\frac {125\,{\left (1-2\,x\right )}^{9/2}}{32} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 32.66, size = 70, normalized size = 0.89 \[ \frac {125 \left (1 - 2 x\right )^{\frac {9}{2}}}{32} - \frac {12675 \left (1 - 2 x\right )^{\frac {7}{2}}}{224} + \frac {5711 \left (1 - 2 x\right )^{\frac {5}{2}}}{16} - \frac {21439 \left (1 - 2 x\right )^{\frac {3}{2}}}{16} + \frac {144837 \sqrt {1 - 2 x}}{32} + \frac {65219}{32 \sqrt {1 - 2 x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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