Optimal. Leaf size=16 \[ -\frac{\sqrt{a+\frac{b}{x^2}}}{b} \]
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Rubi [A] time = 0.0056214, 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} \[ -\frac{\sqrt{a+\frac{b}{x^2}}}{b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{1}{\sqrt{a+\frac{b}{x^2}} x^3} \, dx &=-\frac{\sqrt{a+\frac{b}{x^2}}}{b}\\ \end{align*}
Mathematica [A] time = 0.0085518, size = 16, normalized size = 1. \[ -\frac{\sqrt{a+\frac{b}{x^2}}}{b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 29, normalized size = 1.8 \begin{align*} -{\frac{a{x}^{2}+b}{b{x}^{2}}{\frac{1}{\sqrt{{\frac{a{x}^{2}+b}{{x}^{2}}}}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.965009, size = 19, normalized size = 1.19 \begin{align*} -\frac{\sqrt{a + \frac{b}{x^{2}}}}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.45811, size = 35, normalized size = 2.19 \begin{align*} -\frac{\sqrt{\frac{a x^{2} + b}{x^{2}}}}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.7236, size = 26, normalized size = 1.62 \begin{align*} \begin{cases} - \frac{\sqrt{a + \frac{b}{x^{2}}}}{b} & \text{for}\: b \neq 0 \\- \frac{1}{2 \sqrt{a} x^{2}} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12839, size = 19, normalized size = 1.19 \begin{align*} -\frac{\sqrt{a + \frac{b}{x^{2}}}}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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