Optimal. Leaf size=40 \[ -\frac {5}{12} (1-2 x)^{9/2}+\frac {17}{7} (1-2 x)^{7/2}-\frac {77}{20} (1-2 x)^{5/2} \]
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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} \[ -\frac {5}{12} (1-2 x)^{9/2}+\frac {17}{7} (1-2 x)^{7/2}-\frac {77}{20} (1-2 x)^{5/2} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int (1-2 x)^{3/2} (2+3 x) (3+5 x) \, dx &=\int \left (\frac {77}{4} (1-2 x)^{3/2}-17 (1-2 x)^{5/2}+\frac {15}{4} (1-2 x)^{7/2}\right ) \, dx\\ &=-\frac {77}{20} (1-2 x)^{5/2}+\frac {17}{7} (1-2 x)^{7/2}-\frac {5}{12} (1-2 x)^{9/2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 23, normalized size = 0.58 \[ -\frac {1}{105} (1-2 x)^{5/2} \left (175 x^2+335 x+193\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 29, normalized size = 0.72 \[ -\frac {1}{105} \, {\left (700 \, x^{4} + 640 \, x^{3} - 393 \, x^{2} - 437 \, x + 193\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.07, size = 49, normalized size = 1.22 \[ -\frac {5}{12} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} - \frac {17}{7} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {77}{20} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} \]
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 \[ -\frac {\left (175 x^{2}+335 x +193\right ) \left (-2 x +1\right )^{\frac {5}{2}}}{105} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 28, normalized size = 0.70 \[ -\frac {5}{12} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} + \frac {17}{7} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {77}{20} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} \]
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 \[ -\frac {{\left (1-2\,x\right )}^{5/2}\,\left (2040\,x+175\,{\left (2\,x-1\right )}^2+597\right )}{420} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 7.33, size = 34, normalized size = 0.85 \[ - \frac {5 \left (1 - 2 x\right )^{\frac {9}{2}}}{12} + \frac {17 \left (1 - 2 x\right )^{\frac {7}{2}}}{7} - \frac {77 \left (1 - 2 x\right )^{\frac {5}{2}}}{20} \]
Verification of antiderivative is not currently implemented for this CAS.
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