Optimal. Leaf size=27 \[ \frac{3}{28} \left (x^4+1\right )^{7/3}-\frac{3}{16} \left (x^4+1\right )^{4/3} \]
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Rubi [A] time = 0.0102084, antiderivative size = 27, normalized size of antiderivative = 1., 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} \[ \frac{3}{28} \left (x^4+1\right )^{7/3}-\frac{3}{16} \left (x^4+1\right )^{4/3} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int x^7 \sqrt [3]{1+x^4} \, dx &=\frac{1}{4} \operatorname{Subst}\left (\int x \sqrt [3]{1+x} \, dx,x,x^4\right )\\ &=\frac{1}{4} \operatorname{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*}
Mathematica [A] time = 0.0062148, size = 20, normalized size = 0.74 \[ \frac{3}{112} \left (x^4+1\right )^{4/3} \left (4 x^4-3\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 17, normalized size = 0.6 \begin{align*}{\frac{12\,{x}^{4}-9}{112} \left ({x}^{4}+1 \right ) ^{{\frac{4}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.956257, size = 26, normalized size = 0.96 \begin{align*} \frac{3}{28} \,{\left (x^{4} + 1\right )}^{\frac{7}{3}} - \frac{3}{16} \,{\left (x^{4} + 1\right )}^{\frac{4}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.41467, size = 55, normalized size = 2.04 \begin{align*} \frac{3}{112} \,{\left (4 \, x^{8} + x^{4} - 3\right )}{\left (x^{4} + 1\right )}^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.972573, size = 41, normalized size = 1.52 \begin{align*} \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13798, size = 26, normalized size = 0.96 \begin{align*} \frac{3}{28} \,{\left (x^{4} + 1\right )}^{\frac{7}{3}} - \frac{3}{16} \,{\left (x^{4} + 1\right )}^{\frac{4}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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