Optimal. Leaf size=40 \[ -\frac {15}{44} (1-2 x)^{11/2}+\frac {17}{9} (1-2 x)^{9/2}-\frac {11}{4} (1-2 x)^{7/2} \]
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Rubi [A] time = 0.01, antiderivative size = 40, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \[ -\frac {15}{44} (1-2 x)^{11/2}+\frac {17}{9} (1-2 x)^{9/2}-\frac {11}{4} (1-2 x)^{7/2} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int (1-2 x)^{5/2} (2+3 x) (3+5 x) \, dx &=\int \left (\frac {77}{4} (1-2 x)^{5/2}-17 (1-2 x)^{7/2}+\frac {15}{4} (1-2 x)^{9/2}\right ) \, dx\\ &=-\frac {11}{4} (1-2 x)^{7/2}+\frac {17}{9} (1-2 x)^{9/2}-\frac {15}{44} (1-2 x)^{11/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 23, normalized size = 0.58 \[ -\frac {1}{99} (1-2 x)^{7/2} \left (135 x^2+239 x+119\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.93, size = 34, normalized size = 0.85 \[ \frac {1}{99} \, {\left (1080 \, x^{5} + 292 \, x^{4} - 1106 \, x^{3} - 129 \, x^{2} + 475 \, x - 119\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.92, size = 49, normalized size = 1.22 \[ \frac {15}{44} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {17}{9} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {11}{4} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 20, normalized size = 0.50 \[ -\frac {\left (135 x^{2}+239 x +119\right ) \left (-2 x +1\right )^{\frac {7}{2}}}{99} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 28, normalized size = 0.70 \[ -\frac {15}{44} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {17}{9} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {11}{4} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 23, normalized size = 0.58 \[ -\frac {{\left (1-2\,x\right )}^{7/2}\,\left (1496\,x+135\,{\left (2\,x-1\right )}^2+341\right )}{396} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.55, size = 85, normalized size = 2.12 \[ \frac {120 x^{5} \sqrt {1 - 2 x}}{11} + \frac {292 x^{4} \sqrt {1 - 2 x}}{99} - \frac {1106 x^{3} \sqrt {1 - 2 x}}{99} - \frac {43 x^{2} \sqrt {1 - 2 x}}{33} + \frac {475 x \sqrt {1 - 2 x}}{99} - \frac {119 \sqrt {1 - 2 x}}{99} \]
Verification of antiderivative is not currently implemented for this CAS.
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