Optimal. Leaf size=16 \[ -\frac {1}{6 b \left (a+b x^3\right )^2} \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {261} \[ -\frac {1}{6 b \left (a+b x^3\right )^2} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int \frac {x^2}{\left (a+b x^3\right )^3} \, dx &=-\frac {1}{6 b \left (a+b x^3\right )^2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \[ -\frac {1}{6 b \left (a+b x^3\right )^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.45, size = 26, normalized size = 1.62 \[ -\frac {1}{6 \, {\left (b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 14, normalized size = 0.88 \[ -\frac {1}{6 \, {\left (b x^{3} + a\right )}^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 15, normalized size = 0.94 \[ -\frac {1}{6 \left (b \,x^{3}+a \right )^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.35, size = 14, normalized size = 0.88 \[ -\frac {1}{6 \, {\left (b x^{3} + a\right )}^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.94, size = 28, normalized size = 1.75 \[ -\frac {1}{6\,a^2\,b+12\,a\,b^2\,x^3+6\,b^3\,x^6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.32, size = 27, normalized size = 1.69 \[ - \frac {1}{6 a^{2} b + 12 a b^{2} x^{3} + 6 b^{3} x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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