Optimal. Leaf size=13 \[ -\frac {1}{8 \left (a^4+x^4\right )^2} \]
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Rubi [A]
time = 0.00, antiderivative size = 13, 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}{8 \left (a^4+x^4\right )^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 267
Rubi steps
\begin {align*} \int \frac {x^3}{\left (a^4+x^4\right )^3} \, dx &=-\frac {1}{8 \left (a^4+x^4\right )^2}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} -\frac {1}{8 \left (a^4+x^4\right )^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 12, normalized size = 0.92
method | result | size |
gosper | \(-\frac {1}{8 \left (a^{4}+x^{4}\right )^{2}}\) | \(12\) |
derivativedivides | \(-\frac {1}{8 \left (a^{4}+x^{4}\right )^{2}}\) | \(12\) |
default | \(-\frac {1}{8 \left (a^{4}+x^{4}\right )^{2}}\) | \(12\) |
norman | \(-\frac {1}{8 \left (a^{4}+x^{4}\right )^{2}}\) | \(12\) |
risch | \(-\frac {1}{8 \left (a^{4}+x^{4}\right )^{2}}\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 1.99, size = 11, normalized size = 0.85 \begin {gather*} -\frac {1}{8 \, {\left (a^{4} + x^{4}\right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.49, size = 19, normalized size = 1.46 \begin {gather*} -\frac {1}{8 \, {\left (a^{8} + 2 \, a^{4} x^{4} + x^{8}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.11, size = 20, normalized size = 1.54 \begin {gather*} - \frac {1}{8 a^{8} + 16 a^{4} x^{4} + 8 x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.53, size = 11, normalized size = 0.85 \begin {gather*} -\frac {1}{8 \, {\left (a^{4} + x^{4}\right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.20, size = 11, normalized size = 0.85 \begin {gather*} -\frac {1}{8\,{\left (a^4+x^4\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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