Optimal. Leaf size=12 \[ 2 x \sqrt {\frac {b}{x}} \]
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Rubi [A] time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {15, 30} \begin {gather*} 2 x \sqrt {\frac {b}{x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \sqrt {\frac {b}{x}} \, dx &=\left (\sqrt {\frac {b}{x}} \sqrt {x}\right ) \int \frac {1}{\sqrt {x}} \, dx\\ &=2 \sqrt {\frac {b}{x}} x\\ \end {align*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 1.00 \begin {gather*} 2 x \sqrt {\frac {b}{x}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 12, normalized size = 1.00 \begin {gather*} 2 x \sqrt {\frac {b}{x}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.97, size = 10, normalized size = 0.83 \begin {gather*} 2 \, x \sqrt {\frac {b}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 9, normalized size = 0.75 \begin {gather*} 2 \, \sqrt {b x} \mathrm {sgn}\relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 11, normalized size = 0.92 \begin {gather*} 2 \sqrt {\frac {b}{x}}\, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.28, size = 10, normalized size = 0.83 \begin {gather*} 2 \, x \sqrt {\frac {b}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.97, size = 10, normalized size = 0.83 \begin {gather*} 2\,x\,\sqrt {\frac {b}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 14, normalized size = 1.17 \begin {gather*} 2 \sqrt {b} x \sqrt {\frac {1}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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