Optimal. Leaf size=27 \[ \frac{5}{6} (1-2 x)^{3/2}-\frac{11}{2} \sqrt{1-2 x} \]
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Rubi [A] time = 0.0054607, 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} \[ \frac{5}{6} (1-2 x)^{3/2}-\frac{11}{2} \sqrt{1-2 x} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{3+5 x}{\sqrt{1-2 x}} \, dx &=\int \left (\frac{11}{2 \sqrt{1-2 x}}-\frac{5}{2} \sqrt{1-2 x}\right ) \, dx\\ &=-\frac{11}{2} \sqrt{1-2 x}+\frac{5}{6} (1-2 x)^{3/2}\\ \end{align*}
Mathematica [A] time = 0.0051807, size = 18, normalized size = 0.67 \[ -\frac{1}{3} \sqrt{1-2 x} (5 x+14) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 15, normalized size = 0.6 \begin{align*} -{\frac{14+5\,x}{3}\sqrt{1-2\,x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.5814, size = 26, normalized size = 0.96 \begin{align*} \frac{5}{6} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{11}{2} \, \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.4103, size = 43, normalized size = 1.59 \begin{align*} -\frac{1}{3} \,{\left (5 \, x + 14\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.860873, size = 88, normalized size = 3.26 \begin{align*} \begin{cases} - \frac{\sqrt{5} i \left (x + \frac{3}{5}\right ) \sqrt{10 x - 5}}{3} - \frac{11 \sqrt{5} i \sqrt{10 x - 5}}{15} & \text{for}\: \frac{10 \left |{x + \frac{3}{5}}\right |}{11} > 1 \\- \frac{\sqrt{5} \sqrt{5 - 10 x} \left (x + \frac{3}{5}\right )}{3} - \frac{11 \sqrt{5} \sqrt{5 - 10 x}}{15} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.91708, size = 26, normalized size = 0.96 \begin{align*} \frac{5}{6} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{11}{2} \, \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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