Optimal. Leaf size=16 \[ -\frac {3 \left (x^4+1\right )^{4/3}}{8 x^8} \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {446, 74} \begin {gather*} -\frac {3 \left (x^4+1\right )^{4/3}}{8 x^8} \end {gather*}
Antiderivative was successfully verified.
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Rule 74
Rule 446
Rubi steps
\begin {align*} \int \frac {\sqrt [3]{1+x^4} \left (3+x^4\right )}{x^9} \, dx &=\frac {1}{4} \operatorname {Subst}\left (\int \frac {\sqrt [3]{1+x} (3+x)}{x^3} \, dx,x,x^4\right )\\ &=-\frac {3 \left (1+x^4\right )^{4/3}}{8 x^8}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 16, normalized size = 1.00 \begin {gather*} -\frac {3 \left (x^4+1\right )^{4/3}}{8 x^8} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.04, size = 16, normalized size = 1.00 \begin {gather*} -\frac {3 \left (1+x^4\right )^{4/3}}{8 x^8} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 12, normalized size = 0.75 \begin {gather*} -\frac {3 \, {\left (x^{4} + 1\right )}^{\frac {4}{3}}}{8 \, x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.55, size = 12, normalized size = 0.75 \begin {gather*} -\frac {3 \, {\left (x^{4} + 1\right )}^{\frac {4}{3}}}{8 \, x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 13, normalized size = 0.81
method | result | size |
gosper | \(-\frac {3 \left (x^{4}+1\right )^{\frac {4}{3}}}{8 x^{8}}\) | \(13\) |
trager | \(-\frac {3 \left (x^{4}+1\right )^{\frac {4}{3}}}{8 x^{8}}\) | \(13\) |
risch | \(-\frac {3 \left (x^{8}+2 x^{4}+1\right )}{8 \left (x^{4}+1\right )^{\frac {2}{3}} x^{8}}\) | \(23\) |
meijerg | \(-\frac {\frac {3 \Gamma \left (\frac {2}{3}\right )}{x^{4}}-\left (\frac {\pi \sqrt {3}}{6}-\frac {3 \ln \relax (3)}{2}-1+4 \ln \relax (x )\right ) \Gamma \left (\frac {2}{3}\right )+\frac {\hypergeom \left (\left [1, 1, \frac {5}{3}\right ], \left [2, 3\right ], -x^{4}\right ) \Gamma \left (\frac {2}{3}\right ) x^{4}}{3}}{12 \Gamma \left (\frac {2}{3}\right )}-\frac {\frac {3 \Gamma \left (\frac {2}{3}\right )}{2 x^{8}}+\frac {\Gamma \left (\frac {2}{3}\right )}{x^{4}}+\frac {\left (\frac {\pi \sqrt {3}}{6}-\frac {3 \ln \relax (3)}{2}+4 \ln \relax (x )\right ) \Gamma \left (\frac {2}{3}\right )}{3}-\frac {5 \hypergeom \left (\left [1, 1, \frac {8}{3}\right ], \left [2, 4\right ], -x^{4}\right ) \Gamma \left (\frac {2}{3}\right ) x^{4}}{27}}{4 \Gamma \left (\frac {2}{3}\right )}\) | \(115\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.59, size = 50, normalized size = 3.12 \begin {gather*} \frac {{\left (x^{4} + 1\right )}^{\frac {4}{3}} + 2 \, {\left (x^{4} + 1\right )}^{\frac {1}{3}}}{8 \, {\left (2 \, x^{4} - {\left (x^{4} + 1\right )}^{2} + 1\right )}} - \frac {{\left (x^{4} + 1\right )}^{\frac {1}{3}}}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.23, size = 12, normalized size = 0.75 \begin {gather*} -\frac {3\,{\left (x^4+1\right )}^{4/3}}{8\,x^8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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