Optimal. Leaf size=21 \[ \frac {2 \sqrt {x} \sqrt {a+\frac {b}{x}}}{a} \]
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Rubi [A] time = 0.01, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {264} \[ \frac {2 \sqrt {x} \sqrt {a+\frac {b}{x}}}{a} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin {align*} \int \frac {1}{\sqrt {a+\frac {b}{x}} \sqrt {x}} \, dx &=\frac {2 \sqrt {a+\frac {b}{x}} \sqrt {x}}{a}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 1.00 \[ \frac {2 \sqrt {x} \sqrt {a+\frac {b}{x}}}{a} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 19, normalized size = 0.90 \[ \frac {2 \, \sqrt {x} \sqrt {\frac {a x + b}{x}}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 21, normalized size = 1.00 \[ \frac {2 \, \sqrt {a x + b}}{a} - \frac {2 \, \sqrt {b}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 25, normalized size = 1.19 \[ \frac {2 a x +2 b}{a \sqrt {\frac {a x +b}{x}}\, \sqrt {x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.03, size = 17, normalized size = 0.81 \[ \frac {2 \, \sqrt {a + \frac {b}{x}} \sqrt {x}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.41, size = 17, normalized size = 0.81 \[ \frac {2\,\sqrt {x}\,\sqrt {a+\frac {b}{x}}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.72, size = 17, normalized size = 0.81 \[ \frac {2 \sqrt {b} \sqrt {\frac {a x}{b} + 1}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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