Optimal. Leaf size=16 \[ \frac{1}{4 b \left (a+\frac{b}{x^2}\right )^2} \]
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Rubi [A] time = 0.0038042, 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} \[ \frac{1}{4 b \left (a+\frac{b}{x^2}\right )^2} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{1}{\left (a+\frac{b}{x^2}\right )^3 x^3} \, dx &=\frac{1}{4 b \left (a+\frac{b}{x^2}\right )^2}\\ \end{align*}
Mathematica [A] time = 0.0062335, size = 24, normalized size = 1.5 \[ -\frac{2 a x^2+b}{4 a^2 \left (a x^2+b\right )^2} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.006, size = 31, normalized size = 1.9 \begin{align*}{\frac{b}{4\,{a}^{2} \left ( a{x}^{2}+b \right ) ^{2}}}-{\frac{1}{2\,{a}^{2} \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 = 1.03117, size = 19, normalized size = 1.19 \begin{align*} \frac{1}{4 \,{\left (a + \frac{b}{x^{2}}\right )}^{2} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.38718, size = 73, normalized size = 4.56 \begin{align*} -\frac{2 \, a x^{2} + b}{4 \,{\left (a^{4} x^{4} + 2 \, a^{3} b x^{2} + a^{2} b^{2}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.550227, size = 36, normalized size = 2.25 \begin{align*} - \frac{2 a x^{2} + b}{4 a^{4} x^{4} + 8 a^{3} b x^{2} + 4 a^{2} b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16542, size = 30, normalized size = 1.88 \begin{align*} -\frac{2 \, a x^{2} + b}{4 \,{\left (a x^{2} + b\right )}^{2} a^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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