Optimal. Leaf size=14 \[ \frac {x}{2 \sqrt {\frac {b}{x^2}}} \]
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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} \[ \frac {x}{2 \sqrt {\frac {b}{x^2}}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {1}{\sqrt {\frac {b}{x^2}}} \, dx &=\frac {\int x \, dx}{\sqrt {\frac {b}{x^2}} x}\\ &=\frac {x}{2 \sqrt {\frac {b}{x^2}}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \[ \frac {x}{2 \sqrt {\frac {b}{x^2}}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.72, size = 15, normalized size = 1.07 \[ \frac {x^{3} \sqrt {\frac {b}{x^{2}}}}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 12, normalized size = 0.86 \[ \frac {x^{2}}{2 \, \sqrt {b} \mathrm {sgn}\relax (x)} \]
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 \[ \frac {x}{2 \sqrt {\frac {b}{x^{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.30, size = 10, normalized size = 0.71 \[ \frac {x}{2 \, \sqrt {\frac {b}{x^{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.93, size = 13, normalized size = 0.93 \[ \frac {x^3\,\sqrt {\frac {1}{x^2}}}{2\,\sqrt {b}} \]
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 \[ \frac {x}{2 \sqrt {b} \sqrt {\frac {1}{x^{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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