Optimal. Leaf size=10 \[ -\frac{2}{x (x+1)} \]
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Rubi [A] time = 0.0103235, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.15, Rules used = {1594, 27, 74} \[ -\frac{2}{x (x+1)} \]
Antiderivative was successfully verified.
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Rule 1594
Rule 27
Rule 74
Rubi steps
\begin{align*} \int \frac{2+4 x}{x^2+2 x^3+x^4} \, dx &=\int \frac{2+4 x}{x^2 \left (1+2 x+x^2\right )} \, dx\\ &=\int \frac{2+4 x}{x^2 (1+x)^2} \, dx\\ &=-\frac{2}{x (1+x)}\\ \end{align*}
Mathematica [A] time = 0.005241, size = 9, normalized size = 0.9 \[ -\frac{2}{x^2+x} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 14, normalized size = 1.4 \begin{align*} 2\, \left ( 1+x \right ) ^{-1}-2\,{x}^{-1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.976928, size = 12, normalized size = 1.2 \begin{align*} -\frac{2}{x^{2} + x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.940711, size = 19, normalized size = 1.9 \begin{align*} -\frac{2}{x^{2} + x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.081098, size = 7, normalized size = 0.7 \begin{align*} - \frac{2}{x^{2} + x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10217, size = 12, normalized size = 1.2 \begin{align*} -\frac{2}{x^{2} + x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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