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}
\begin {gather*} \frac {2 x}{3 \sqrt {\frac {b}{x}}} \end {gather*}
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 \begin {gather*} \frac {2 x}{3 \sqrt {\frac {b}{x}}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 11, normalized size = 0.79
method | result | size |
gosper | \(\frac {2 x}{3 \sqrt {\frac {b}{x}}}\) | \(11\) |
default | \(\frac {2 x}{3 \sqrt {\frac {b}{x}}}\) | \(11\) |
risch | \(\frac {2 x}{3 \sqrt {\frac {b}{x}}}\) | \(11\) |
trager | \(\frac {2 \sqrt {\frac {b}{x}}\, x^{2}}{3 b}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 10, normalized size = 0.71 \begin {gather*} \frac {2 \, x}{3 \, \sqrt {\frac {b}{x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 15, normalized size = 1.07 \begin {gather*} \frac {2 \, x^{2} \sqrt {\frac {b}{x}}}{3 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.16, size = 10, normalized size = 0.71 \begin {gather*} \frac {2 x}{3 \sqrt {\frac {b}{x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.09, size = 15, normalized size = 1.07 \begin {gather*} \frac {2 \, \sqrt {b x} x}{3 \, b \mathrm {sgn}\left (x\right )} \end {gather*}
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 \begin {gather*} \frac {2\,x^2\,\sqrt {\frac {b}{x}}}{3\,b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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