Optimal. Leaf size=27 \[ \frac{5}{2} \sqrt{1-2 x}+\frac{11}{2 \sqrt{1-2 x}} \]
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Rubi [A] time = 0.0059016, 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} \[ \frac{5}{2} \sqrt{1-2 x}+\frac{11}{2 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{3+5 x}{(1-2 x)^{3/2}} \, dx &=\int \left (\frac{11}{2 (1-2 x)^{3/2}}-\frac{5}{2 \sqrt{1-2 x}}\right ) \, dx\\ &=\frac{11}{2 \sqrt{1-2 x}}+\frac{5}{2} \sqrt{1-2 x}\\ \end{align*}
Mathematica [A] time = 0.0059007, size = 15, normalized size = 0.56 \[ \frac{8-5 x}{\sqrt{1-2 x}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 15, normalized size = 0.6 \begin{align*} -{(-8+5\,x){\frac{1}{\sqrt{1-2\,x}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.07534, size = 26, normalized size = 0.96 \begin{align*} \frac{5}{2} \, \sqrt{-2 \, x + 1} + \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 = 1.6033, size = 49, normalized size = 1.81 \begin{align*} \frac{{\left (5 \, x - 8\right )} \sqrt{-2 \, x + 1}}{2 \, x - 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.342798, size = 20, normalized size = 0.74 \begin{align*} - \frac{5 x}{\sqrt{1 - 2 x}} + \frac{8}{\sqrt{1 - 2 x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.32777, size = 26, normalized size = 0.96 \begin{align*} \frac{5}{2} \, \sqrt{-2 \, x + 1} + \frac{11}{2 \, \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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