Optimal. Leaf size=5 \[ -\log \left (\cot ^{-1}(x)\right ) \]
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Rubi [A] time = 0.0199193, antiderivative size = 5, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083, Rules used = {4883} \[ -\log \left (\cot ^{-1}(x)\right ) \]
Antiderivative was successfully verified.
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Rule 4883
Rubi steps
\begin{align*} \int \frac{1}{\left (1+x^2\right ) \cot ^{-1}(x)} \, dx &=-\log \left (\cot ^{-1}(x)\right )\\ \end{align*}
Mathematica [A] time = 0.0226783, size = 5, normalized size = 1. \[ -\log \left (\cot ^{-1}(x)\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.019, size = 6, normalized size = 1.2 \begin{align*} -\ln \left ({\rm arccot} \left (x\right ) \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.946703, size = 7, normalized size = 1.4 \begin{align*} -\log \left (\operatorname{arccot}\left (x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.76909, size = 23, normalized size = 4.6 \begin{align*} -\log \left (\operatorname{arccot}\left (x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.344778, size = 5, normalized size = 1. \begin{align*} - \log{\left (\operatorname{acot}{\left (x \right )} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09545, size = 11, normalized size = 2.2 \begin{align*} -\log \left ({\left | \arctan \left (\frac{1}{x}\right ) \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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