Optimal. Leaf size=17 \[ \frac{1}{8 b \left (a-b x^2\right )^4} \]
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Rubi [A] time = 0.0027673, 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} \[ \frac{1}{8 b \left (a-b x^2\right )^4} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{x}{\left (a-b x^2\right )^5} \, dx &=\frac{1}{8 b \left (a-b x^2\right )^4}\\ \end{align*}
Mathematica [A] time = 0.0030155, size = 17, normalized size = 1. \[ \frac{1}{8 b \left (a-b x^2\right )^4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 17, normalized size = 1. \begin{align*}{\frac{1}{8\,b \left ( b{x}^{2}-a \right ) ^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.10508, size = 22, normalized size = 1.29 \begin{align*} \frac{1}{8 \,{\left (b x^{2} - a\right )}^{4} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.16939, size = 93, normalized size = 5.47 \begin{align*} \frac{1}{8 \,{\left (b^{5} x^{8} - 4 \, a b^{4} x^{6} + 6 \, a^{2} b^{3} x^{4} - 4 \, a^{3} b^{2} x^{2} + a^{4} b\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.730105, size = 49, normalized size = 2.88 \begin{align*} \frac{1}{8 a^{4} b - 32 a^{3} b^{2} x^{2} + 48 a^{2} b^{3} x^{4} - 32 a b^{4} x^{6} + 8 b^{5} x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.82081, size = 22, normalized size = 1.29 \begin{align*} \frac{1}{8 \,{\left (b x^{2} - a\right )}^{4} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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