Optimal. Leaf size=13 \[ -\frac {3}{4 \sqrt [3]{x^4+1}} \]
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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 = {261} \[ -\frac {3}{4 \sqrt [3]{x^4+1}} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int \frac {x^3}{\left (1+x^4\right )^{4/3}} \, dx &=-\frac {3}{4 \sqrt [3]{1+x^4}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 1.00 \[ -\frac {3}{4 \sqrt [3]{x^4+1}} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.05, size = 9, normalized size = 0.69 \[ -\frac {3}{4 \, {\left (x^{4} + 1\right )}^{\frac {1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 9, normalized size = 0.69 \[ -\frac {3}{4 \, {\left (x^{4} + 1\right )}^{\frac {1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 10, normalized size = 0.77 \[ -\frac {3}{4 \left (x^{4}+1\right )^{\frac {1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.35, size = 9, normalized size = 0.69 \[ -\frac {3}{4 \, {\left (x^{4} + 1\right )}^{\frac {1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.10, size = 9, normalized size = 0.69 \[ -\frac {3}{4\,{\left (x^4+1\right )}^{1/3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.56, size = 12, normalized size = 0.92 \[ - \frac {3}{4 \sqrt [3]{x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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