Optimal. Leaf size=16 \[ \frac {1}{4 b \left (a+\frac {b}{x^2}\right )^2} \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, size = 24, normalized size = 1.50 \[ -\frac {2 a x^2+b}{4 a^2 \left (a x^2+b\right )^2} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.92, size = 36, normalized size = 2.25 \[ -\frac {2 \, a x^{2} + b}{4 \, {\left (a^{4} x^{4} + 2 \, a^{3} b x^{2} + a^{2} b^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 22, normalized size = 1.38 \[ -\frac {2 \, a x^{2} + b}{4 \, {\left (a x^{2} + b\right )}^{2} a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.01, size = 31, normalized size = 1.94 \[ \frac {b}{4 \left (a \,x^{2}+b \right )^{2} a^{2}}-\frac {1}{2 \left (a \,x^{2}+b \right ) a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.87, size = 14, normalized size = 0.88 \[ \frac {1}{4 \, {\left (a + \frac {b}{x^{2}}\right )}^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.08, size = 37, normalized size = 2.31 \[ -\frac {\frac {b}{4\,a^2}+\frac {x^2}{2\,a}}{a^2\,x^4+2\,a\,b\,x^2+b^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.29, size = 36, normalized size = 2.25 \[ \frac {- 2 a x^{2} - b}{4 a^{4} x^{4} + 8 a^{3} b x^{2} + 4 a^{2} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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