Optimal. Leaf size=16 \[ -\frac{1}{4 a \left (a x^2+b\right )^2} \]
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Rubi [A] time = 0.0050669, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {263, 261} \[ -\frac{1}{4 a \left (a x^2+b\right )^2} \]
Antiderivative was successfully verified.
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Rule 263
Rule 261
Rubi steps
\begin{align*} \int \frac{1}{\left (a+\frac{b}{x^2}\right )^3 x^5} \, dx &=\int \frac{x}{\left (b+a x^2\right )^3} \, dx\\ &=-\frac{1}{4 a \left (b+a x^2\right )^2}\\ \end{align*}
Mathematica [A] time = 0.0024111, size = 16, normalized size = 1. \[ -\frac{1}{4 a \left (a x^2+b\right )^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 15, normalized size = 0.9 \begin{align*} -{\frac{1}{4\,a \left ( a{x}^{2}+b \right ) ^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.994418, size = 35, normalized size = 2.19 \begin{align*} -\frac{1}{4 \,{\left (a^{3} x^{4} + 2 \, a^{2} b x^{2} + a b^{2}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.37883, size = 51, normalized size = 3.19 \begin{align*} -\frac{1}{4 \,{\left (a^{3} x^{4} + 2 \, a^{2} b x^{2} + a b^{2}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.514413, size = 27, normalized size = 1.69 \begin{align*} - \frac{1}{4 a^{3} x^{4} + 8 a^{2} b x^{2} + 4 a b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16098, size = 19, normalized size = 1.19 \begin{align*} -\frac{1}{4 \,{\left (a x^{2} + b\right )}^{2} a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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