Optimal. Leaf size=17 \[ \frac{1}{2 b \left (a-b x^2\right )} \]
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Rubi [A] time = 0.0028674, 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} \[ \frac{1}{2 b \left (a-b x^2\right )} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{x}{\left (a-b x^2\right )^2} \, dx &=\frac{1}{2 b \left (a-b x^2\right )}\\ \end{align*}
Mathematica [A] time = 0.002445, size = 17, normalized size = 1. \[ \frac{1}{2 b \left (a-b x^2\right )} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 17, normalized size = 1. \begin{align*} -{\frac{1}{2\,b \left ( b{x}^{2}-a \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.08676, size = 22, normalized size = 1.29 \begin{align*} -\frac{1}{2 \,{\left (b x^{2} - a\right )} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.21364, size = 30, normalized size = 1.76 \begin{align*} -\frac{1}{2 \,{\left (b^{2} x^{2} - a b\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.30581, size = 15, normalized size = 0.88 \begin{align*} - \frac{1}{- 2 a b + 2 b^{2} x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.58455, size = 22, normalized size = 1.29 \begin{align*} -\frac{1}{2 \,{\left (b x^{2} - a\right )} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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