Optimal. Leaf size=10 \[ \frac{x}{x^2+x+1} \]
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Rubi [A] time = 0.0107474, antiderivative size = 10, 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} \[ \frac{x}{x^2+x+1} \]
Antiderivative was successfully verified.
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Rule 1588
Rubi steps
\begin{align*} \int \frac{1-x^2}{\left (1+x+x^2\right )^2} \, dx &=\frac{x}{1+x+x^2}\\ \end{align*}
Mathematica [A] time = 0.0052611, size = 10, normalized size = 1. \[ \frac{x}{x^2+x+1} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.042, size = 11, normalized size = 1.1 \begin{align*}{\frac{x}{{x}^{2}+x+1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02832, size = 14, normalized size = 1.4 \begin{align*} \frac{x}{x^{2} + x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.6145, size = 23, normalized size = 2.3 \begin{align*} \frac{x}{x^{2} + x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.086572, size = 7, normalized size = 0.7 \begin{align*} \frac{x}{x^{2} + x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.20656, size = 11, normalized size = 1.1 \begin{align*} \frac{1}{x + \frac{1}{x} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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