Optimal. Leaf size=14 \[ -2 \log \left (\sqrt{4-x}+1\right ) \]
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Rubi [A] time = 0.0185971, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062, Rules used = {31} \[ -2 \log \left (\sqrt{4-x}+1\right ) \]
Antiderivative was successfully verified.
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Rule 31
Rubi steps
\begin{align*} \int \frac{1}{4+\sqrt{4-x}-x} \, dx &=-\left (2 \operatorname{Subst}\left (\int \frac{1}{1+x} \, dx,x,\sqrt{4-x}\right )\right )\\ &=-2 \log \left (1+\sqrt{4-x}\right )\\ \end{align*}
Mathematica [A] time = 0.0052837, size = 14, normalized size = 1. \[ -2 \log \left (\sqrt{4-x}+1\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.01, size = 18, normalized size = 1.3 \begin{align*} -\ln \left ( -3+x \right ) -2\,{\it Artanh} \left ( \sqrt{4-x} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.950734, size = 16, normalized size = 1.14 \begin{align*} -2 \, \log \left (\sqrt{-x + 4} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.40136, size = 35, normalized size = 2.5 \begin{align*} -2 \, \log \left (\sqrt{-x + 4} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 2.10782, size = 32, normalized size = 2.29 \begin{align*} \log{\left (2 \sqrt{4 - x} \right )} - \log{\left (2 \sqrt{4 - x} + 2 \right )} - \log{\left (x - \sqrt{4 - x} - 4 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14667, size = 16, normalized size = 1.14 \begin{align*} -2 \, \log \left (\sqrt{-x + 4} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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