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 = {267}
\begin {gather*} -\frac {1}{6 b \left (a+b x^3\right )^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 267
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 \begin {gather*} -\frac {1}{6 b \left (a+b x^3\right )^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 15, normalized size = 0.94
method | result | size |
gosper | \(-\frac {1}{6 b \left (b \,x^{3}+a \right )^{2}}\) | \(15\) |
derivativedivides | \(-\frac {1}{6 b \left (b \,x^{3}+a \right )^{2}}\) | \(15\) |
default | \(-\frac {1}{6 b \left (b \,x^{3}+a \right )^{2}}\) | \(15\) |
norman | \(-\frac {1}{6 b \left (b \,x^{3}+a \right )^{2}}\) | \(15\) |
risch | \(-\frac {1}{6 b \left (b \,x^{3}+a \right )^{2}}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 14, normalized size = 0.88 \begin {gather*} -\frac {1}{6 \, {\left (b x^{3} + a\right )}^{2} b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 26, normalized size = 1.62 \begin {gather*} -\frac {1}{6 \, {\left (b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.13, size = 27, normalized size = 1.69 \begin {gather*} - \frac {1}{6 a^{2} b + 12 a b^{2} x^{3} + 6 b^{3} x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.84, size = 14, normalized size = 0.88 \begin {gather*} -\frac {1}{6 \, {\left (b x^{3} + a\right )}^{2} b} \end {gather*}
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 \begin {gather*} -\frac {1}{6\,a^2\,b+12\,a\,b^2\,x^3+6\,b^3\,x^6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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