Optimal. Leaf size=10 \[ -\frac {2}{x (x+1)} \]
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Rubi [A] time = 0.01, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.150, Rules used = {1594, 27, 74} \begin {gather*} -\frac {2}{x (x+1)} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 74
Rule 1594
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*}
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Mathematica [A] time = 0.01, size = 9, normalized size = 0.90 \begin {gather*} -\frac {2}{x^2+x} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2+4 x}{x^2+2 x^3+x^4} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.19, size = 9, normalized size = 0.90 \begin {gather*} -\frac {2}{x^{2} + x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.26, size = 9, normalized size = 0.90 \begin {gather*} -\frac {2}{x^{2} + x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 1.40 \begin {gather*} -\frac {2}{x}+\frac {2}{x +1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.78, size = 9, normalized size = 0.90 \begin {gather*} -\frac {2}{x^{2} + x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.20, size = 10, normalized size = 1.00 \begin {gather*} -\frac {2}{x\,\left (x+1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 7, normalized size = 0.70 \begin {gather*} - \frac {2}{x^{2} + x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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