Optimal. Leaf size=11 \[ -\frac{x}{x^5+x+1} \]
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Rubi [A] time = 0.0068737, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062, Rules used = {1588} \[ -\frac{x}{x^5+x+1} \]
Antiderivative was successfully verified.
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Rule 1588
Rubi steps
\begin{align*} \int \frac{-1+4 x^5}{\left (1+x+x^5\right )^2} \, dx &=-\frac{x}{1+x+x^5}\\ \end{align*}
Mathematica [A] time = 0.0065788, size = 11, normalized size = 1. \[ -\frac{x}{x^5+x+1} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.009, size = 41, normalized size = 3.7 \begin{align*} -{\frac{-3\,{x}^{2}+5\,x-1}{7\,{x}^{3}-7\,{x}^{2}+7}}+{\frac{-3\,x-1}{7\,{x}^{2}+7\,x+7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02207, size = 15, normalized size = 1.36 \begin{align*} -\frac{x}{x^{5} + x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.35098, size = 24, normalized size = 2.18 \begin{align*} -\frac{x}{x^{5} + x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.119274, size = 8, normalized size = 0.73 \begin{align*} - \frac{x}{x^{5} + x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.24403, size = 15, normalized size = 1.36 \begin{align*} -\frac{x}{x^{5} + x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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