Optimal. Leaf size=13 \[ \frac {3}{28} \left (1+x^7\right )^{4/3} \]
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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}{28} \left (x^7+1\right )^{4/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 267
Rubi steps
\begin {align*} \int x^6 \sqrt [3]{1+x^7} \, dx &=\frac {3}{28} \left (1+x^7\right )^{4/3}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 13, normalized size = 1.00 \begin {gather*} \frac {3}{28} \left (1+x^7\right )^{4/3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.07, size = 10, normalized size = 0.77
method | result | size |
derivativedivides | \(\frac {3 \left (x^{7}+1\right )^{\frac {4}{3}}}{28}\) | \(10\) |
default | \(\frac {3 \left (x^{7}+1\right )^{\frac {4}{3}}}{28}\) | \(10\) |
risch | \(\frac {3 \left (x^{7}+1\right )^{\frac {4}{3}}}{28}\) | \(10\) |
trager | \(\left (\frac {3}{28}+\frac {3 x^{7}}{28}\right ) \left (x^{7}+1\right )^{\frac {1}{3}}\) | \(16\) |
meijerg | \(\frac {x^{7} \hypergeom \left (\left [-\frac {1}{3}, 1\right ], \left [2\right ], -x^{7}\right )}{7}\) | \(17\) |
gosper | \(\frac {3 \left (1+x \right ) \left (x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x +1\right ) \left (x^{7}+1\right )^{\frac {1}{3}}}{28}\) | \(37\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 5.63, size = 9, normalized size = 0.69 \begin {gather*} \frac {3}{28} \, {\left (x^{7} + 1\right )}^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.82, size = 9, normalized size = 0.69 \begin {gather*} \frac {3}{28} \, {\left (x^{7} + 1\right )}^{\frac {4}{3}} \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. 26 vs.
\(2 (10) = 20\).
time = 0.12, size = 26, normalized size = 2.00 \begin {gather*} \frac {3 x^{7} \sqrt [3]{x^{7} + 1}}{28} + \frac {3 \sqrt [3]{x^{7} + 1}}{28} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.66, size = 9, normalized size = 0.69 \begin {gather*} \frac {3}{28} \, {\left (x^{7} + 1\right )}^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.29, size = 9, normalized size = 0.69 \begin {gather*} \frac {3\,{\left (x^7+1\right )}^{4/3}}{28} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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