Optimal. Leaf size=12 \[ -\tan ^{-1}\left (\sqrt{3}-x\right ) \]
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Rubi [A] time = 0.0086108, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {618, 204} \[ -\tan ^{-1}\left (\sqrt{3}-x\right ) \]
Antiderivative was successfully verified.
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Rule 618
Rule 204
Rubi steps
\begin{align*} \int \frac{1}{4-2 \sqrt{3} x+x^2} \, dx &=-\left (2 \operatorname{Subst}\left (\int \frac{1}{-4-x^2} \, dx,x,-2 \sqrt{3}+2 x\right )\right )\\ &=-\tan ^{-1}\left (\sqrt{3}-x\right )\\ \end{align*}
Mathematica [A] time = 0.0142963, size = 12, normalized size = 1. \[ -\tan ^{-1}\left (\sqrt{3}-x\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.052, size = 9, normalized size = 0.8 \begin{align*} \arctan \left ( x-\sqrt{3} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.70056, size = 11, normalized size = 0.92 \begin{align*} \arctan \left (x - \sqrt{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.27582, size = 28, normalized size = 2.33 \begin{align*} \arctan \left (x - \sqrt{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.247866, size = 7, normalized size = 0.58 \begin{align*} \operatorname{atan}{\left (x - \sqrt{3} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.30593, size = 11, normalized size = 0.92 \begin{align*} \arctan \left (x - \sqrt{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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