Optimal. Leaf size=16 \[ \frac{1}{2 b \left (a+\frac{b}{x^2}\right )} \]
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Rubi [A] time = 0.003838, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {261} \[ \frac{1}{2 b \left (a+\frac{b}{x^2}\right )} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{1}{\left (a+\frac{b}{x^2}\right )^2 x^3} \, dx &=\frac{1}{2 b \left (a+\frac{b}{x^2}\right )}\\ \end{align*}
Mathematica [A] time = 0.0020879, size = 16, normalized size = 1. \[ -\frac{1}{2 a \left (a x^2+b\right )} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 15, normalized size = 0.9 \begin{align*} -{\frac{1}{2\,a \left ( a{x}^{2}+b \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.987966, size = 19, normalized size = 1.19 \begin{align*} \frac{1}{2 \,{\left (a + \frac{b}{x^{2}}\right )} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.41691, size = 30, normalized size = 1.88 \begin{align*} -\frac{1}{2 \,{\left (a^{2} x^{2} + a b\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.399971, size = 15, normalized size = 0.94 \begin{align*} - \frac{1}{2 a^{2} x^{2} + 2 a b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14598, size = 19, normalized size = 1.19 \begin{align*} -\frac{1}{2 \,{\left (a x^{2} + b\right )} a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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