Optimal. Leaf size=14 \[ \frac {2 x}{3 \sqrt {\frac {b}{x}}} \]
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Rubi [A] time = 0.00, antiderivative size = 14, 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} \[ \frac {2 x}{3 \sqrt {\frac {b}{x}}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {1}{\sqrt {\frac {b}{x}}} \, dx &=\frac {\int \sqrt {x} \, dx}{\sqrt {\frac {b}{x}} \sqrt {x}}\\ &=\frac {2 x}{3 \sqrt {\frac {b}{x}}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \[ \frac {2 x}{3 \sqrt {\frac {b}{x}}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.88, size = 15, normalized size = 1.07 \[ \frac {2 \, x^{2} \sqrt {\frac {b}{x}}}{3 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 15, normalized size = 1.07 \[ \frac {2 \, \sqrt {b x} x}{3 \, b \mathrm {sgn}\relax (x)} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 11, normalized size = 0.79 \[ \frac {2 x}{3 \sqrt {\frac {b}{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.33, size = 10, normalized size = 0.71 \[ \frac {2 \, x}{3 \, \sqrt {\frac {b}{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.95, size = 15, normalized size = 1.07 \[ \frac {2\,x^2\,\sqrt {\frac {b}{x}}}{3\,b} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.39, size = 15, normalized size = 1.07 \[ \frac {2 x}{3 \sqrt {b} \sqrt {\frac {1}{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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