Optimal. Leaf size=8 \[ -\frac{1}{2} \cot ^{-1}(x)^2 \]
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Rubi [A] time = 0.0115701, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1, Rules used = {4885} \[ -\frac{1}{2} \cot ^{-1}(x)^2 \]
Antiderivative was successfully verified.
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Rule 4885
Rubi steps
\begin{align*} \int \frac{\cot ^{-1}(x)}{1+x^2} \, dx &=-\frac{1}{2} \cot ^{-1}(x)^2\\ \end{align*}
Mathematica [A] time = 0.0031552, size = 8, normalized size = 1. \[ -\frac{1}{2} \cot ^{-1}(x)^2 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.02, size = 7, normalized size = 0.9 \begin{align*} -{\frac{ \left ({\rm arccot} \left (x\right ) \right ) ^{2}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.977856, size = 8, normalized size = 1. \begin{align*} -\frac{1}{2} \, \operatorname{arccot}\left (x\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.92167, size = 24, normalized size = 3. \begin{align*} -\frac{1}{2} \, \operatorname{arccot}\left (x\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.695324, size = 7, normalized size = 0.88 \begin{align*} - \frac{\operatorname{acot}^{2}{\left (x \right )}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10768, size = 11, normalized size = 1.38 \begin{align*} -\frac{1}{2} \, \arctan \left (\frac{1}{x}\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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