Optimal. Leaf size=12 \[ -\tan ^{-1}\left (\sqrt {3}-x\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 12, normalized size of antiderivative = 1.00, 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 204
Rule 618
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*}
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Mathematica [A] time = 0.01, size = 12, normalized size = 1.00 \[ -\tan ^{-1}\left (\sqrt {3}-x\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.90, size = 8, normalized size = 0.67 \[ \arctan \left (x - \sqrt {3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.41, size = 8, normalized size = 0.67 \[ \arctan \left (x - \sqrt {3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.10, size = 9, normalized size = 0.75 \[ \arctan \left (x -\sqrt {3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 2.97, size = 8, normalized size = 0.67 \[ \arctan \left (x - \sqrt {3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.27, size = 8, normalized size = 0.67 \[ \mathrm {atan}\left (x-\sqrt {3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 7, normalized size = 0.58 \[ \operatorname {atan}{\left (x - \sqrt {3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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