Optimal. Leaf size=13 \[ \frac {1}{7} \left (-1+x^4\right )^{7/4} \]
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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 {1}{7} \left (x^4-1\right )^{7/4} \end {gather*}
Antiderivative was successfully verified.
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Rule 267
Rubi steps
\begin {align*} \int x^3 \left (-1+x^4\right )^{3/4} \, dx &=\frac {1}{7} \left (-1+x^4\right )^{7/4}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 13, normalized size = 1.00 \begin {gather*} \frac {1}{7} \left (-1+x^4\right )^{7/4} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.28, size = 10, normalized size = 0.77
method | result | size |
derivativedivides | \(\frac {\left (x^{4}-1\right )^{\frac {7}{4}}}{7}\) | \(10\) |
default | \(\frac {\left (x^{4}-1\right )^{\frac {7}{4}}}{7}\) | \(10\) |
risch | \(\frac {\left (x^{4}-1\right )^{\frac {7}{4}}}{7}\) | \(10\) |
trager | \(\left (\frac {x^{4}}{7}-\frac {1}{7}\right ) \left (x^{4}-1\right )^{\frac {3}{4}}\) | \(16\) |
gosper | \(\frac {\left (-1+x \right ) \left (1+x \right ) \left (x^{2}+1\right ) \left (x^{4}-1\right )^{\frac {3}{4}}}{7}\) | \(21\) |
meijerg | \(\frac {\mathrm {signum}\left (x^{4}-1\right )^{\frac {3}{4}} x^{4} \hypergeom \left (\left [-\frac {3}{4}, 1\right ], \left [2\right ], x^{4}\right )}{4 \left (-\mathrm {signum}\left (x^{4}-1\right )\right )^{\frac {3}{4}}}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{7} \, {\left (x^{4} - 1\right )}^{\frac {7}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{7} \, {\left (x^{4} - 1\right )}^{\frac {7}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 22 vs.
\(2 (8) = 16\).
time = 0.18, size = 22, normalized size = 1.69 \begin {gather*} \frac {x^{4} \left (x^{4} - 1\right )^{\frac {3}{4}}}{7} - \frac {\left (x^{4} - 1\right )^{\frac {3}{4}}}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{7} \, {\left (x^{4} - 1\right )}^{\frac {7}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.13, size = 9, normalized size = 0.69 \begin {gather*} \frac {{\left (x^4-1\right )}^{7/4}}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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