Optimal. Leaf size=16 \[ -\frac{2 \sqrt{a+\frac{b}{x}}}{b} \]
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Rubi [A] time = 0.0051254, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {261} \[ -\frac{2 \sqrt{a+\frac{b}{x}}}{b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{1}{\sqrt{a+\frac{b}{x}} x^2} \, dx &=-\frac{2 \sqrt{a+\frac{b}{x}}}{b}\\ \end{align*}
Mathematica [A] time = 0.0059379, size = 16, normalized size = 1. \[ -\frac{2 \sqrt{a+\frac{b}{x}}}{b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 25, normalized size = 1.6 \begin{align*} -2\,{\frac{ax+b}{bx}{\frac{1}{\sqrt{{\frac{ax+b}{x}}}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.18039, size = 19, normalized size = 1.19 \begin{align*} -\frac{2 \, \sqrt{a + \frac{b}{x}}}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.59524, size = 32, normalized size = 2. \begin{align*} -\frac{2 \, \sqrt{\frac{a x + b}{x}}}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.741817, size = 22, normalized size = 1.38 \begin{align*} \begin{cases} - \frac{2 \sqrt{a + \frac{b}{x}}}{b} & \text{for}\: b \neq 0 \\- \frac{1}{\sqrt{a} x} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10221, size = 19, normalized size = 1.19 \begin{align*} -\frac{2 \, \sqrt{a + \frac{b}{x}}}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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