Optimal. Leaf size=13 \[ -\frac{3}{14 \left (x^7+1\right )^{2/3}} \]
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Rubi [A] time = 0.0029647, 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} \[ -\frac{3}{14 \left (x^7+1\right )^{2/3}} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{x^6}{\left (1+x^7\right )^{5/3}} \, dx &=-\frac{3}{14 \left (1+x^7\right )^{2/3}}\\ \end{align*}
Mathematica [A] time = 0.0026527, size = 13, normalized size = 1. \[ -\frac{3}{14 \left (x^7+1\right )^{2/3}} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.004, 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 ) }{14} \left ({x}^{7}+1 \right ) ^{-{\frac{5}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.942658, size = 12, normalized size = 0.92 \begin{align*} -\frac{3}{14 \,{\left (x^{7} + 1\right )}^{\frac{2}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.77936, size = 31, normalized size = 2.38 \begin{align*} -\frac{3}{14 \,{\left (x^{7} + 1\right )}^{\frac{2}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.572686, size = 12, normalized size = 0.92 \begin{align*} - \frac{3}{14 \left (x^{7} + 1\right )^{\frac{2}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06213, size = 12, normalized size = 0.92 \begin{align*} -\frac{3}{14 \,{\left (x^{7} + 1\right )}^{\frac{2}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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