Optimal. Leaf size=20 \[ \frac{x^4}{4 a \left (a-b x^2\right )^2} \]
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Rubi [A] time = 0.003635, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071, Rules used = {264} \[ \frac{x^4}{4 a \left (a-b x^2\right )^2} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{x^3}{\left (a-b x^2\right )^3} \, dx &=\frac{x^4}{4 a \left (a-b x^2\right )^2}\\ \end{align*}
Mathematica [A] time = 0.0085554, size = 25, normalized size = 1.25 \[ -\frac{a-2 b x^2}{4 b^2 \left (a-b x^2\right )^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 35, normalized size = 1.8 \begin{align*}{\frac{1}{2\,{b}^{2} \left ( b{x}^{2}-a \right ) }}+{\frac{a}{4\,{b}^{2} \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 = 2.67729, size = 51, normalized size = 2.55 \begin{align*} \frac{2 \, b x^{2} - a}{4 \,{\left (b^{4} x^{4} - 2 \, a b^{3} x^{2} + a^{2} b^{2}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.2255, size = 72, normalized size = 3.6 \begin{align*} \frac{2 \, b x^{2} - a}{4 \,{\left (b^{4} x^{4} - 2 \, a b^{3} x^{2} + a^{2} b^{2}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.632648, size = 34, normalized size = 1.7 \begin{align*} \frac{- a + 2 b x^{2}}{4 a^{2} b^{2} - 8 a b^{3} x^{2} + 4 b^{4} x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.219, size = 35, normalized size = 1.75 \begin{align*} \frac{2 \, b x^{2} - a}{4 \,{\left (b x^{2} - a\right )}^{2} b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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