Optimal. Leaf size=5 \[ \log \left (\tan ^{-1}(x)+2\right ) \]
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Rubi [A] time = 0.0245949, antiderivative size = 5, normalized size of antiderivative = 1., 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 = {4882} \[ \log \left (\tan ^{-1}(x)+2\right ) \]
Antiderivative was successfully verified.
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Rule 4882
Rubi steps
\begin{align*} \int \frac{1}{\left (1+x^2\right ) \left (2+\tan ^{-1}(x)\right )} \, dx &=\log \left (2+\tan ^{-1}(x)\right )\\ \end{align*}
Mathematica [A] time = 0.0293372, size = 5, normalized size = 1. \[ \log \left (\tan ^{-1}(x)+2\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.036, size = 6, normalized size = 1.2 \begin{align*} \ln \left ( 2+\arctan \left ( x \right ) \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.953525, size = 7, normalized size = 1.4 \begin{align*} \log \left (\arctan \left (x\right ) + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.9855, size = 27, normalized size = 5.4 \begin{align*} \log \left (\arctan \left (x\right ) + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.349717, size = 5, normalized size = 1. \begin{align*} \log{\left (\operatorname{atan}{\left (x \right )} + 2 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10889, size = 7, normalized size = 1.4 \begin{align*} \log \left (\arctan \left (x\right ) + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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