Optimal. Leaf size=17 \[ \frac {1}{8 b \left (a-b x^2\right )^4} \]
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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} \[ \frac {1}{8 b \left (a-b x^2\right )^4} \]
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*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \[ \frac {1}{8 b \left (a-b x^2\right )^4} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.81, size = 48, normalized size = 2.82 \[ \frac {1}{8 \, {\left (b^{5} x^{8} - 4 \, a b^{4} x^{6} + 6 \, a^{2} b^{3} x^{4} - 4 \, a^{3} b^{2} x^{2} + a^{4} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.62, size = 16, normalized size = 0.94 \[ \frac {1}{8 \, {\left (b x^{2} - a\right )}^{4} b} \]
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 \[ \frac {1}{8 \left (b \,x^{2}-a \right )^{4} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.31, size = 16, normalized size = 0.94 \[ \frac {1}{8 \, {\left (b x^{2} - a\right )}^{4} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.69, size = 48, normalized size = 2.82 \[ \frac {1}{8\,a^4\,b-32\,a^3\,b^2\,x^2+48\,a^2\,b^3\,x^4-32\,a\,b^4\,x^6+8\,b^5\,x^8} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.40, size = 49, normalized size = 2.88 \[ \frac {1}{8 a^{4} b - 32 a^{3} b^{2} x^{2} + 48 a^{2} b^{3} x^{4} - 32 a b^{4} x^{6} + 8 b^{5} x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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