Optimal. Leaf size=27 \[ \frac{1}{2} (1-2 x)^{5/2}-\frac{11}{6} (1-2 x)^{3/2} \]
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Rubi [A] time = 0.0054496, 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} \[ \frac{1}{2} (1-2 x)^{5/2}-\frac{11}{6} (1-2 x)^{3/2} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \sqrt{1-2 x} (3+5 x) \, dx &=\int \left (\frac{11}{2} \sqrt{1-2 x}-\frac{5}{2} (1-2 x)^{3/2}\right ) \, dx\\ &=-\frac{11}{6} (1-2 x)^{3/2}+\frac{1}{2} (1-2 x)^{5/2}\\ \end{align*}
Mathematica [A] time = 0.0068064, size = 18, normalized size = 0.67 \[ -\frac{1}{3} (1-2 x)^{3/2} (3 x+4) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 15, normalized size = 0.6 \begin{align*} -{\frac{3\,x+4}{3} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.54555, size = 26, normalized size = 0.96 \begin{align*} \frac{1}{2} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{11}{6} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.42848, size = 51, normalized size = 1.89 \begin{align*} \frac{1}{3} \,{\left (6 \, x^{2} + 5 \, x - 4\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.875609, size = 138, normalized size = 5.11 \begin{align*} \begin{cases} \frac{2 \sqrt{5} i \left (x + \frac{3}{5}\right )^{2} \sqrt{10 x - 5}}{5} - \frac{11 \sqrt{5} i \left (x + \frac{3}{5}\right ) \sqrt{10 x - 5}}{75} - \frac{121 \sqrt{5} i \sqrt{10 x - 5}}{375} & \text{for}\: \frac{10 \left |{x + \frac{3}{5}}\right |}{11} > 1 \\\frac{2 \sqrt{5} \sqrt{5 - 10 x} \left (x + \frac{3}{5}\right )^{2}}{5} - \frac{11 \sqrt{5} \sqrt{5 - 10 x} \left (x + \frac{3}{5}\right )}{75} - \frac{121 \sqrt{5} \sqrt{5 - 10 x}}{375} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.67709, size = 35, normalized size = 1.3 \begin{align*} \frac{1}{2} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{11}{6} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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