Optimal. Leaf size=17 \[ \frac {1}{4 b \left (a-b x^2\right )^2} \]
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Rubi [A] time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \[ \frac {1}{4 b \left (a-b x^2\right )^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.98, size = 26, normalized size = 1.53 \[ \frac {1}{4 \, {\left (b^{3} x^{4} - 2 \, a b^{2} x^{2} + a^{2} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.61, size = 16, normalized size = 0.94 \[ \frac {1}{4 \, {\left (b x^{2} - a\right )}^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 17, normalized size = 1.00 \[ \frac {1}{4 \left (b \,x^{2}-a \right )^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.34, size = 16, normalized size = 0.94 \[ \frac {1}{4 \, {\left (b x^{2} - a\right )}^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 26, normalized size = 1.53 \[ \frac {1}{4\,a^2\,b-8\,a\,b^2\,x^2+4\,b^3\,x^4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.24, size = 26, normalized size = 1.53 \[ \frac {1}{4 a^{2} b - 8 a b^{2} x^{2} + 4 b^{3} x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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