Optimal. Leaf size=25 \[ \frac {3}{160} \left (x^4+1\right )^{2/3} \left (5 x^8+2 x^4-3\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 27, normalized size of antiderivative = 1.08, 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 = {266, 43} \begin {gather*} \frac {3}{32} \left (x^4+1\right )^{8/3}-\frac {3}{20} \left (x^4+1\right )^{5/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int x^7 \left (1+x^4\right )^{2/3} \, dx &=\frac {1}{4} \operatorname {Subst}\left (\int x (1+x)^{2/3} \, dx,x,x^4\right )\\ &=\frac {1}{4} \operatorname {Subst}\left (\int \left (-(1+x)^{2/3}+(1+x)^{5/3}\right ) \, dx,x,x^4\right )\\ &=-\frac {3}{20} \left (1+x^4\right )^{5/3}+\frac {3}{32} \left (1+x^4\right )^{8/3}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 20, normalized size = 0.80 \begin {gather*} \frac {3}{160} \left (x^4+1\right )^{5/3} \left (5 x^4-3\right ) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.03, size = 20, normalized size = 0.80 \begin {gather*} \frac {3}{160} \left (x^4+1\right )^{5/3} \left (5 x^4-3\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.38, size = 21, normalized size = 0.84 \begin {gather*} \frac {3}{160} \, {\left (5 \, x^{8} + 2 \, x^{4} - 3\right )} {\left (x^{4} + 1\right )}^{\frac {2}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.45, size = 19, normalized size = 0.76 \begin {gather*} \frac {3}{32} \, {\left (x^{4} + 1\right )}^{\frac {8}{3}} - \frac {3}{20} \, {\left (x^{4} + 1\right )}^{\frac {5}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 17, normalized size = 0.68 \begin {gather*} \frac {3 \left (x^{4}+1\right )^{\frac {5}{3}} \left (5 x^{4}-3\right )}{160} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 19, normalized size = 0.76 \begin {gather*} \frac {3}{32} \, {\left (x^{4} + 1\right )}^{\frac {8}{3}} - \frac {3}{20} \, {\left (x^{4} + 1\right )}^{\frac {5}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.22, size = 20, normalized size = 0.80 \begin {gather*} {\left (x^4+1\right )}^{2/3}\,\left (\frac {3\,x^8}{32}+\frac {3\,x^4}{80}-\frac {9}{160}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.00, size = 41, normalized size = 1.64 \begin {gather*} \frac {3 x^{8} \left (x^{4} + 1\right )^{\frac {2}{3}}}{32} + \frac {3 x^{4} \left (x^{4} + 1\right )^{\frac {2}{3}}}{80} - \frac {9 \left (x^{4} + 1\right )^{\frac {2}{3}}}{160} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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