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 = 0.0051879, antiderivative size = 27, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0084097, 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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Maple [A] time = 0.002, size = 15, normalized size = 0.6 \begin{align*} -{\frac{25\,x+26}{35} \left ( 1-2\,x \right ) ^{{\frac{5}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.2933, size = 26, normalized size = 0.96 \begin{align*} \frac{5}{14} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{11}{10} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.40494, size = 70, normalized size = 2.59 \begin{align*} -\frac{1}{35} \,{\left (100 \, x^{3} + 4 \, x^{2} - 79 \, x + 26\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.357208, size = 54, normalized size = 2. \begin{align*} - \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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.02132, size = 45, normalized size = 1.67 \begin{align*} -\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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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