Optimal. Leaf size=27 \[ -\frac {3}{16} \left (1+x^4\right )^{4/3}+\frac {3}{28} \left (1+x^4\right )^{7/3} \]
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Rubi [A]
time = 0.01, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {272, 45}
\begin {gather*} \frac {3}{28} \left (x^4+1\right )^{7/3}-\frac {3}{16} \left (x^4+1\right )^{4/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rule 272
Rubi steps
\begin {align*} \int x^7 \sqrt [3]{1+x^4} \, dx &=\frac {1}{4} \text {Subst}\left (\int x \sqrt [3]{1+x} \, dx,x,x^4\right )\\ &=\frac {1}{4} \text {Subst}\left (\int \left (-\sqrt [3]{1+x}+(1+x)^{4/3}\right ) \, dx,x,x^4\right )\\ &=-\frac {3}{16} \left (1+x^4\right )^{4/3}+\frac {3}{28} \left (1+x^4\right )^{7/3}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 20, normalized size = 0.74 \begin {gather*} \frac {3}{112} \left (1+x^4\right )^{4/3} \left (-3+4 x^4\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.16, size = 17, normalized size = 0.63
method | result | size |
gosper | \(\frac {3 \left (x^{4}+1\right )^{\frac {4}{3}} \left (4 x^{4}-3\right )}{112}\) | \(17\) |
meijerg | \(\frac {x^{8} \hypergeom \left (\left [-\frac {1}{3}, 2\right ], \left [3\right ], -x^{4}\right )}{8}\) | \(17\) |
risch | \(\frac {3 \left (x^{4}+1\right )^{\frac {1}{3}} \left (4 x^{8}+x^{4}-3\right )}{112}\) | \(20\) |
trager | \(\left (\frac {3}{28} x^{8}+\frac {3}{112} x^{4}-\frac {9}{112}\right ) \left (x^{4}+1\right )^{\frac {1}{3}}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 19, normalized size = 0.70 \begin {gather*} \frac {3}{28} \, {\left (x^{4} + 1\right )}^{\frac {7}{3}} - \frac {3}{16} \, {\left (x^{4} + 1\right )}^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 19, normalized size = 0.70 \begin {gather*} \frac {3}{112} \, {\left (4 \, x^{8} + x^{4} - 3\right )} {\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 = 0.15, size = 41, normalized size = 1.52 \begin {gather*} \frac {3 x^{8} \sqrt [3]{x^{4} + 1}}{28} + \frac {3 x^{4} \sqrt [3]{x^{4} + 1}}{112} - \frac {9 \sqrt [3]{x^{4} + 1}}{112} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.04, size = 19, normalized size = 0.70 \begin {gather*} \frac {3}{28} \, {\left (x^{4} + 1\right )}^{\frac {7}{3}} - \frac {3}{16} \, {\left (x^{4} + 1\right )}^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.10, size = 16, normalized size = 0.59 \begin {gather*} \frac {3\,{\left (x^4+1\right )}^{4/3}\,\left (4\,x^4-3\right )}{112} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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