Optimal. Leaf size=53 \[ \frac {15}{8} (1-2 x)^{3/2}-\frac {309}{8} \sqrt {1-2 x}-\frac {707}{8 \sqrt {1-2 x}}+\frac {539}{24 (1-2 x)^{3/2}} \]
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Rubi [A] time = 0.01, antiderivative size = 53, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {77} \[ \frac {15}{8} (1-2 x)^{3/2}-\frac {309}{8} \sqrt {1-2 x}-\frac {707}{8 \sqrt {1-2 x}}+\frac {539}{24 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(2+3 x)^2 (3+5 x)}{(1-2 x)^{5/2}} \, dx &=\int \left (\frac {539}{8 (1-2 x)^{5/2}}-\frac {707}{8 (1-2 x)^{3/2}}+\frac {309}{8 \sqrt {1-2 x}}-\frac {45}{8} \sqrt {1-2 x}\right ) \, dx\\ &=\frac {539}{24 (1-2 x)^{3/2}}-\frac {707}{8 \sqrt {1-2 x}}-\frac {309}{8} \sqrt {1-2 x}+\frac {15}{8} (1-2 x)^{3/2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 28, normalized size = 0.53 \[ -\frac {45 x^3+396 x^2-960 x+308}{3 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.89, size = 36, normalized size = 0.68 \[ -\frac {{\left (45 \, x^{3} + 396 \, x^{2} - 960 \, x + 308\right )} \sqrt {-2 \, x + 1}}{3 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.24, size = 40, normalized size = 0.75 \[ \frac {15}{8} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {309}{8} \, \sqrt {-2 \, x + 1} - \frac {7 \, {\left (303 \, x - 113\right )}}{12 \, {\left (2 \, x - 1\right )} \sqrt {-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 25, normalized size = 0.47 \[ -\frac {45 x^{3}+396 x^{2}-960 x +308}{3 \left (-2 x +1\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.61, size = 33, normalized size = 0.62 \[ \frac {15}{8} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {309}{8} \, \sqrt {-2 \, x + 1} + \frac {7 \, {\left (303 \, x - 113\right )}}{12 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.19, size = 38, normalized size = 0.72 \[ \frac {927\,{\left (2\,x-1\right )}^2-4242\,x+45\,{\left (2\,x-1\right )}^3+1582}{\sqrt {1-2\,x}\,\left (48\,x-24\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.71, size = 102, normalized size = 1.92 \[ \frac {45 x^{3}}{6 x \sqrt {1 - 2 x} - 3 \sqrt {1 - 2 x}} + \frac {396 x^{2}}{6 x \sqrt {1 - 2 x} - 3 \sqrt {1 - 2 x}} - \frac {960 x}{6 x \sqrt {1 - 2 x} - 3 \sqrt {1 - 2 x}} + \frac {308}{6 x \sqrt {1 - 2 x} - 3 \sqrt {1 - 2 x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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