Optimal. Leaf size=17 \[ \frac{1}{4 b \left (a-b x^2\right )^2} \]
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Rubi [A] time = 0.0030325, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083, Rules used = {261} \[ \frac{1}{4 b \left (a-b x^2\right )^2} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{x}{\left (a-b x^2\right )^3} \, dx &=\frac{1}{4 b \left (a-b x^2\right )^2}\\ \end{align*}
Mathematica [A] time = 0.0020358, size = 17, normalized size = 1. \[ \frac{1}{4 b \left (a-b x^2\right )^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 17, normalized size = 1. \begin{align*}{\frac{1}{4\,b \left ( b{x}^{2}-a \right ) ^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.51478, size = 22, normalized size = 1.29 \begin{align*} \frac{1}{4 \,{\left (b x^{2} - a\right )}^{2} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.1873, size = 50, normalized size = 2.94 \begin{align*} \frac{1}{4 \,{\left (b^{3} x^{4} - 2 \, a b^{2} x^{2} + a^{2} b\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.389559, size = 26, normalized size = 1.53 \begin{align*} \frac{1}{4 a^{2} b - 8 a b^{2} x^{2} + 4 b^{3} x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.89824, size = 22, normalized size = 1.29 \begin{align*} \frac{1}{4 \,{\left (b x^{2} - a\right )}^{2} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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