Optimal. Leaf size=92 \[ -\frac {3375}{704} (1-2 x)^{11/2}+\frac {1275}{16} (1-2 x)^{9/2}-\frac {260055}{448} (1-2 x)^{7/2}+\frac {98209}{40} (1-2 x)^{5/2}-\frac {444983}{64} (1-2 x)^{3/2}+\frac {302379}{16} \sqrt {1-2 x}+\frac {456533}{64 \sqrt {1-2 x}} \]
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Rubi [A] time = 0.02, antiderivative size = 92, 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} \[ -\frac {3375}{704} (1-2 x)^{11/2}+\frac {1275}{16} (1-2 x)^{9/2}-\frac {260055}{448} (1-2 x)^{7/2}+\frac {98209}{40} (1-2 x)^{5/2}-\frac {444983}{64} (1-2 x)^{3/2}+\frac {302379}{16} \sqrt {1-2 x}+\frac {456533}{64 \sqrt {1-2 x}} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^3 (3+5 x)^3}{(1-2 x)^{3/2}} \, dx &=\int \left (\frac {456533}{64 (1-2 x)^{3/2}}-\frac {302379}{16 \sqrt {1-2 x}}+\frac {1334949}{64} \sqrt {1-2 x}-\frac {98209}{8} (1-2 x)^{3/2}+\frac {260055}{64} (1-2 x)^{5/2}-\frac {11475}{16} (1-2 x)^{7/2}+\frac {3375}{64} (1-2 x)^{9/2}\right ) \, dx\\ &=\frac {456533}{64 \sqrt {1-2 x}}+\frac {302379}{16} \sqrt {1-2 x}-\frac {444983}{64} (1-2 x)^{3/2}+\frac {98209}{40} (1-2 x)^{5/2}-\frac {260055}{448} (1-2 x)^{7/2}+\frac {1275}{16} (1-2 x)^{9/2}-\frac {3375}{704} (1-2 x)^{11/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 43, normalized size = 0.47 \[ \frac {-118125 x^6-627375 x^5-1564350 x^4-2569643 x^3-3611453 x^2-8012926 x+8096086}{385 \sqrt {1-2 x}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 46, normalized size = 0.50 \[ \frac {{\left (118125 \, x^{6} + 627375 \, x^{5} + 1564350 \, x^{4} + 2569643 \, x^{3} + 3611453 \, x^{2} + 8012926 \, x - 8096086\right )} \sqrt {-2 \, x + 1}}{385 \, {\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.20, size = 92, normalized size = 1.00 \[ \frac {3375}{704} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {1275}{16} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {260055}{448} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} + \frac {98209}{40} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} - \frac {444983}{64} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + \frac {302379}{16} \, \sqrt {-2 \, x + 1} + \frac {456533}{64 \, \sqrt {-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 40, normalized size = 0.43 \[ -\frac {118125 x^{6}+627375 x^{5}+1564350 x^{4}+2569643 x^{3}+3611453 x^{2}+8012926 x -8096086}{385 \sqrt {-2 x +1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.80, size = 64, normalized size = 0.70 \[ -\frac {3375}{704} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {1275}{16} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {260055}{448} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} + \frac {98209}{40} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - \frac {444983}{64} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + \frac {302379}{16} \, \sqrt {-2 \, x + 1} + \frac {456533}{64 \, \sqrt {-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 64, normalized size = 0.70 \[ \frac {456533}{64\,\sqrt {1-2\,x}}+\frac {302379\,\sqrt {1-2\,x}}{16}-\frac {444983\,{\left (1-2\,x\right )}^{3/2}}{64}+\frac {98209\,{\left (1-2\,x\right )}^{5/2}}{40}-\frac {260055\,{\left (1-2\,x\right )}^{7/2}}{448}+\frac {1275\,{\left (1-2\,x\right )}^{9/2}}{16}-\frac {3375\,{\left (1-2\,x\right )}^{11/2}}{704} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 42.30, size = 82, normalized size = 0.89 \[ - \frac {3375 \left (1 - 2 x\right )^{\frac {11}{2}}}{704} + \frac {1275 \left (1 - 2 x\right )^{\frac {9}{2}}}{16} - \frac {260055 \left (1 - 2 x\right )^{\frac {7}{2}}}{448} + \frac {98209 \left (1 - 2 x\right )^{\frac {5}{2}}}{40} - \frac {444983 \left (1 - 2 x\right )^{\frac {3}{2}}}{64} + \frac {302379 \sqrt {1 - 2 x}}{16} + \frac {456533}{64 \sqrt {1 - 2 x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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