Optimal. Leaf size=27 \[ \frac {5}{14} (1-2 x)^{7/2}-\frac {11}{10} (1-2 x)^{5/2} \]
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Rubi [A] time = 0.01, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {43} \[ \frac {5}{14} (1-2 x)^{7/2}-\frac {11}{10} (1-2 x)^{5/2} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int (1-2 x)^{3/2} (3+5 x) \, dx &=\int \left (\frac {11}{2} (1-2 x)^{3/2}-\frac {5}{2} (1-2 x)^{5/2}\right ) \, dx\\ &=-\frac {11}{10} (1-2 x)^{5/2}+\frac {5}{14} (1-2 x)^{7/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 18, normalized size = 0.67 \[ -\frac {1}{35} (1-2 x)^{5/2} (25 x+26) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.97, size = 24, normalized size = 0.89 \[ -\frac {1}{35} \, {\left (100 \, x^{3} + 4 \, x^{2} - 79 \, x + 26\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.92, size = 33, normalized size = 1.22 \[ -\frac {5}{14} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {11}{10} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 15, normalized size = 0.56 \[ -\frac {\left (25 x +26\right ) \left (-2 x +1\right )^{\frac {5}{2}}}{35} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 19, normalized size = 0.70 \[ \frac {5}{14} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {11}{10} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 14, normalized size = 0.52 \[ -\frac {{\left (1-2\,x\right )}^{5/2}\,\left (50\,x+52\right )}{70} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.38, size = 54, normalized size = 2.00 \[ - \frac {20 x^{3} \sqrt {1 - 2 x}}{7} - \frac {4 x^{2} \sqrt {1 - 2 x}}{35} + \frac {79 x \sqrt {1 - 2 x}}{35} - \frac {26 \sqrt {1 - 2 x}}{35} \]
Verification of antiderivative is not currently implemented for this CAS.
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