Optimal. Leaf size=27 \[ \frac{5}{18} (1-2 x)^{9/2}-\frac{11}{14} (1-2 x)^{7/2} \]
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Rubi [A] time = 0.0048761, 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} \[ \frac{5}{18} (1-2 x)^{9/2}-\frac{11}{14} (1-2 x)^{7/2} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int (1-2 x)^{5/2} (3+5 x) \, dx &=\int \left (\frac{11}{2} (1-2 x)^{5/2}-\frac{5}{2} (1-2 x)^{7/2}\right ) \, dx\\ &=-\frac{11}{14} (1-2 x)^{7/2}+\frac{5}{18} (1-2 x)^{9/2}\\ \end{align*}
Mathematica [A] time = 0.0086448, size = 18, normalized size = 0.67 \[ -\frac{1}{63} (1-2 x)^{7/2} (35 x+32) \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 15, normalized size = 0.6 \begin{align*} -{\frac{35\,x+32}{63} \left ( 1-2\,x \right ) ^{{\frac{7}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.17762, size = 26, normalized size = 0.96 \begin{align*} \frac{5}{18} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{11}{14} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.52107, size = 86, normalized size = 3.19 \begin{align*} \frac{1}{63} \,{\left (280 \, x^{4} - 164 \, x^{3} - 174 \, x^{2} + 157 \, x - 32\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.16103, size = 70, normalized size = 2.59 \begin{align*} \frac{40 x^{4} \sqrt{1 - 2 x}}{9} - \frac{164 x^{3} \sqrt{1 - 2 x}}{63} - \frac{58 x^{2} \sqrt{1 - 2 x}}{21} + \frac{157 x \sqrt{1 - 2 x}}{63} - \frac{32 \sqrt{1 - 2 x}}{63} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.10712, size = 45, normalized size = 1.67 \begin{align*} \frac{5}{18} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{11}{14} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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