Optimal. Leaf size=11 \[ -\frac{x}{\left (x^2+x+1\right )^3} \]
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Rubi [A] time = 0.0076456, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053, Rules used = {1588} \[ -\frac{x}{\left (x^2+x+1\right )^3} \]
Antiderivative was successfully verified.
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Rule 1588
Rubi steps
\begin{align*} \int \frac{-1+2 x+5 x^2}{\left (1+x+x^2\right )^4} \, dx &=-\frac{x}{\left (1+x+x^2\right )^3}\\ \end{align*}
Mathematica [A] time = 0.0060935, size = 11, normalized size = 1. \[ -\frac{x}{\left (x^2+x+1\right )^3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.047, size = 12, normalized size = 1.1 \begin{align*} -{\frac{x}{ \left ({x}^{2}+x+1 \right ) ^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.0292, size = 45, normalized size = 4.09 \begin{align*} -\frac{x}{x^{6} + 3 \, x^{5} + 6 \, x^{4} + 7 \, x^{3} + 6 \, x^{2} + 3 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.62136, size = 70, normalized size = 6.36 \begin{align*} -\frac{x}{x^{6} + 3 \, x^{5} + 6 \, x^{4} + 7 \, x^{3} + 6 \, x^{2} + 3 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.129674, size = 31, normalized size = 2.82 \begin{align*} - \frac{x}{x^{6} + 3 x^{5} + 6 x^{4} + 7 x^{3} + 6 x^{2} + 3 x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.26893, size = 15, normalized size = 1.36 \begin{align*} -\frac{x}{{\left (x^{2} + x + 1\right )}^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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