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 = 0.05, 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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fricas [A] time = 0.38, 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 = 0.00, size = 13, normalized size = 0.81 \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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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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