Optimal. Leaf size=53 \[ \frac {45}{88} (1-2 x)^{11/2}-\frac {103}{24} (1-2 x)^{9/2}+\frac {101}{8} (1-2 x)^{7/2}-\frac {539}{40} (1-2 x)^{5/2} \]
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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} \[ \frac {45}{88} (1-2 x)^{11/2}-\frac {103}{24} (1-2 x)^{9/2}+\frac {101}{8} (1-2 x)^{7/2}-\frac {539}{40} (1-2 x)^{5/2} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int (1-2 x)^{3/2} (2+3 x)^2 (3+5 x) \, dx &=\int \left (\frac {539}{8} (1-2 x)^{3/2}-\frac {707}{8} (1-2 x)^{5/2}+\frac {309}{8} (1-2 x)^{7/2}-\frac {45}{8} (1-2 x)^{9/2}\right ) \, dx\\ &=-\frac {539}{40} (1-2 x)^{5/2}+\frac {101}{8} (1-2 x)^{7/2}-\frac {103}{24} (1-2 x)^{9/2}+\frac {45}{88} (1-2 x)^{11/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 28, normalized size = 0.53 \[ -\frac {1}{165} (1-2 x)^{5/2} \left (675 x^3+1820 x^2+1840 x+764\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 1.18, size = 34, normalized size = 0.64 \[ -\frac {1}{165} \, {\left (2700 \, x^{5} + 4580 \, x^{4} + 755 \, x^{3} - 2484 \, x^{2} - 1216 \, x + 764\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.66, size = 65, normalized size = 1.23 \[ -\frac {45}{88} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} - \frac {103}{24} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} - \frac {101}{8} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {539}{40} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 25, normalized size = 0.47 \[ -\frac {\left (675 x^{3}+1820 x^{2}+1840 x +764\right ) \left (-2 x +1\right )^{\frac {5}{2}}}{165} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 37, normalized size = 0.70 \[ \frac {45}{88} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} - \frac {103}{24} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} + \frac {101}{8} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {539}{40} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 37, normalized size = 0.70 \[ \frac {101\,{\left (1-2\,x\right )}^{7/2}}{8}-\frac {539\,{\left (1-2\,x\right )}^{5/2}}{40}-\frac {103\,{\left (1-2\,x\right )}^{9/2}}{24}+\frac {45\,{\left (1-2\,x\right )}^{11/2}}{88} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 10.30, size = 46, normalized size = 0.87 \[ \frac {45 \left (1 - 2 x\right )^{\frac {11}{2}}}{88} - \frac {103 \left (1 - 2 x\right )^{\frac {9}{2}}}{24} + \frac {101 \left (1 - 2 x\right )^{\frac {7}{2}}}{8} - \frac {539 \left (1 - 2 x\right )^{\frac {5}{2}}}{40} \]
Verification of antiderivative is not currently implemented for this CAS.
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