Optimal. Leaf size=13 \[ \frac{3}{28} \left (x^7+1\right )^{4/3} \]
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Rubi [A] time = 0.0027798, antiderivative size = 13, normalized size of antiderivative = 1., 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 = {261} \[ \frac{3}{28} \left (x^7+1\right )^{4/3} \]
Antiderivative was successfully verified.
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Rule 261
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*}
Mathematica [A] time = 0.0029953, size = 13, normalized size = 1. \[ \frac{3}{28} \left (x^7+1\right )^{4/3} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.006, size = 37, normalized size = 2.9 \begin{align*}{\frac{ \left ( 3+3\,x \right ) \left ({x}^{6}-{x}^{5}+{x}^{4}-{x}^{3}+{x}^{2}-x+1 \right ) }{28}\sqrt [3]{{x}^{7}+1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.937423, size = 12, normalized size = 0.92 \begin{align*} \frac{3}{28} \,{\left (x^{7} + 1\right )}^{\frac{4}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.73788, size = 30, normalized size = 2.31 \begin{align*} \frac{3}{28} \,{\left (x^{7} + 1\right )}^{\frac{4}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.560205, size = 26, normalized size = 2. \begin{align*} \frac{3 x^{7} \sqrt [3]{x^{7} + 1}}{28} + \frac{3 \sqrt [3]{x^{7} + 1}}{28} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06003, size = 12, normalized size = 0.92 \begin{align*} \frac{3}{28} \,{\left (x^{7} + 1\right )}^{\frac{4}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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