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 = 0.01, antiderivative size = 27, normalized size of antiderivative = 1.00, 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} \begin {gather*} \frac {5}{2} \sqrt {1-2 x}+\frac {11}{2 \sqrt {1-2 x}} \end {gather*}
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*}
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Mathematica [A] time = 0.01, size = 15, normalized size = 0.56 \begin {gather*} \frac {8-5 x}{\sqrt {1-2 x}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 22, normalized size = 0.81 \begin {gather*} \frac {5 (1-2 x)+11}{2 \sqrt {1-2 x}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.44, size = 20, normalized size = 0.74 \begin {gather*} \frac {{\left (5 \, x - 8\right )} \sqrt {-2 \, x + 1}}{2 \, x - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.18, size = 19, normalized size = 0.70 \begin {gather*} \frac {5}{2} \, \sqrt {-2 \, x + 1} + \frac {11}{2 \, \sqrt {-2 \, x + 1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 15, normalized size = 0.56 \begin {gather*} -\frac {5 x -8}{\sqrt {-2 x +1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 19, normalized size = 0.70 \begin {gather*} \frac {5}{2} \, \sqrt {-2 \, x + 1} + \frac {11}{2 \, \sqrt {-2 \, x + 1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 14, normalized size = 0.52 \begin {gather*} -\frac {5\,x-8}{\sqrt {1-2\,x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.35, size = 20, normalized size = 0.74 \begin {gather*} - \frac {5 x}{\sqrt {1 - 2 x}} + \frac {8}{\sqrt {1 - 2 x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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