Optimal. Leaf size=7 \[ -\frac {1}{x+1} \]
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Rubi [A] time = 0.00, antiderivative size = 7, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, 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*}
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Mathematica [A] time = 0.00, size = 7, normalized size = 1.00 \[ -\frac {1}{x+1} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 7, normalized size = 1.00 \[ -\frac {1}{x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.05, size = 7, normalized size = 1.00 \[ -\frac {1}{x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 8, normalized size = 1.14 \[ -\frac {1}{x +1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 7, normalized size = 1.00 \[ -\frac {1}{x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 7, normalized size = 1.00 \[ -\frac {1}{x+1} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 5, normalized size = 0.71 \[ - \frac {1}{x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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