Optimal. Leaf size=14 \[ -\frac {1}{4 \left (x^2+2 x+2\right )^2} \]
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Rubi [A] time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {629} \[ -\frac {1}{4 \left (x^2+2 x+2\right )^2} \]
Antiderivative was successfully verified.
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Rule 629
Rubi steps
\begin {align*} \int \frac {1+x}{\left (2+2 x+x^2\right )^3} \, dx &=-\frac {1}{4 \left (2+2 x+x^2\right )^2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 14, normalized size = 1.00 \[ -\frac {1}{4 \left (x^2+2 x+2\right )^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 22, normalized size = 1.57 \[ -\frac {1}{4 \, {\left (x^{4} + 4 \, x^{3} + 8 \, x^{2} + 8 \, x + 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.01, size = 12, normalized size = 0.86 \[ -\frac {1}{4 \, {\left (x^{2} + 2 \, x + 2\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 13, normalized size = 0.93 \[ -\frac {1}{4 \left (x^{2}+2 x +2\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 12, normalized size = 0.86 \[ -\frac {1}{4 \, {\left (x^{2} + 2 \, x + 2\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 12, normalized size = 0.86 \[ -\frac {1}{4\,{\left (x^2+2\,x+2\right )}^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 22, normalized size = 1.57 \[ - \frac {1}{4 x^{4} + 16 x^{3} + 32 x^{2} + 32 x + 16} \]
Verification of antiderivative is not currently implemented for this CAS.
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