Optimal. Leaf size=16 \[ -\frac{\left (a+\frac{b}{x^2}\right )^3}{6 b} \]
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Rubi [A] time = 0.0037366, 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} \[ -\frac{\left (a+\frac{b}{x^2}\right )^3}{6 b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{\left (a+\frac{b}{x^2}\right )^2}{x^3} \, dx &=-\frac{\left (a+\frac{b}{x^2}\right )^3}{6 b}\\ \end{align*}
Mathematica [A] time = 0.0008002, size = 30, normalized size = 1.88 \[ -\frac{a^2}{2 x^2}-\frac{a b}{2 x^4}-\frac{b^2}{6 x^6} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 25, normalized size = 1.6 \begin{align*} -{\frac{ab}{2\,{x}^{4}}}-{\frac{{a}^{2}}{2\,{x}^{2}}}-{\frac{{b}^{2}}{6\,{x}^{6}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00612, size = 19, normalized size = 1.19 \begin{align*} -\frac{{\left (a + \frac{b}{x^{2}}\right )}^{3}}{6 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.38843, size = 54, normalized size = 3.38 \begin{align*} -\frac{3 \, a^{2} x^{4} + 3 \, a b x^{2} + b^{2}}{6 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.326129, size = 26, normalized size = 1.62 \begin{align*} - \frac{3 a^{2} x^{4} + 3 a b x^{2} + b^{2}}{6 x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17065, size = 32, normalized size = 2. \begin{align*} -\frac{3 \, a^{2} x^{4} + 3 \, a b x^{2} + b^{2}}{6 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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