Optimal. Leaf size=7 \[ -\frac{1}{x+1} \]
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Rubi [A] time = 0.0010104, antiderivative size = 7, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2, Rules used = {27, 32} \[ -\frac{1}{x+1} \]
Antiderivative was successfully verified.
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Rule 27
Rule 32
Rubi steps
\begin{align*} \int \frac{1}{1+2 x+x^2} \, dx &=\int \frac{1}{(1+x)^2} \, dx\\ &=-\frac{1}{1+x}\\ \end{align*}
Mathematica [A] time = 0.0008212, size = 7, normalized size = 1. \[ -\frac{1}{x+1} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 8, normalized size = 1.1 \begin{align*} - \left ( 1+x \right ) ^{-1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.924597, size = 9, normalized size = 1.29 \begin{align*} -\frac{1}{x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.02132, size = 16, normalized size = 2.29 \begin{align*} -\frac{1}{x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.070916, size = 5, normalized size = 0.71 \begin{align*} - \frac{1}{x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.0837, size = 9, normalized size = 1.29 \begin{align*} -\frac{1}{x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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