Optimal. Leaf size=16 \[ -\frac{1}{4 b \left (a+b x^2\right )^2} \]
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Rubi [A] time = 0.0028312, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, 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 = 0.0021633, size = 16, 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 = 15, normalized size = 0.9 \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 = 2.11486, size = 19, normalized size = 1.19 \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 = 1.1138, size = 51, normalized size = 3.19 \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 [A] time = 0.420224, size = 27, normalized size = 1.69 \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 = 2.00536, size = 19, normalized size = 1.19 \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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