Optimal. Leaf size=13 \[ -\frac {3}{4 \sqrt [3]{1+x^4}} \]
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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 {3}{4 \sqrt [3]{x^4+1}} \end {gather*}
Antiderivative was successfully verified.
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Rule 267
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 = 0.01, size = 13, normalized size = 1.00 \begin {gather*} -\frac {3}{4 \sqrt [3]{1+x^4}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.15, size = 10, normalized size = 0.77
method | result | size |
gosper | \(-\frac {3}{4 \left (x^{4}+1\right )^{\frac {1}{3}}}\) | \(10\) |
derivativedivides | \(-\frac {3}{4 \left (x^{4}+1\right )^{\frac {1}{3}}}\) | \(10\) |
default | \(-\frac {3}{4 \left (x^{4}+1\right )^{\frac {1}{3}}}\) | \(10\) |
trager | \(-\frac {3}{4 \left (x^{4}+1\right )^{\frac {1}{3}}}\) | \(10\) |
risch | \(-\frac {3}{4 \left (x^{4}+1\right )^{\frac {1}{3}}}\) | \(10\) |
meijerg | \(\frac {x^{4} \hypergeom \left (\left [1, \frac {4}{3}\right ], \left [2\right ], -x^{4}\right )}{4}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 9, normalized size = 0.69 \begin {gather*} -\frac {3}{4 \, {\left (x^{4} + 1\right )}^{\frac {1}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 9, normalized size = 0.69 \begin {gather*} -\frac {3}{4 \, {\left (x^{4} + 1\right )}^{\frac {1}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.16, size = 12, normalized size = 0.92 \begin {gather*} - \frac {3}{4 \sqrt [3]{x^{4} + 1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.96, size = 9, normalized size = 0.69 \begin {gather*} -\frac {3}{4 \, {\left (x^{4} + 1\right )}^{\frac {1}{3}}} \end {gather*}
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 \begin {gather*} -\frac {3}{4\,{\left (x^4+1\right )}^{1/3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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