Optimal. Leaf size=8 \[ -x-\cot (x) \]
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Rubi [A] time = 0.0052417, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 4, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5, Rules used = {3473, 8} \[ -x-\cot (x) \]
Antiderivative was successfully verified.
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Rule 3473
Rule 8
Rubi steps
\begin{align*} \int \cot ^2(x) \, dx &=-\cot (x)-\int 1 \, dx\\ &=-x-\cot (x)\\ \end{align*}
Mathematica [A] time = 0.0022213, size = 8, normalized size = 1. \[ -x-\cot (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 12, normalized size = 1.5 \begin{align*} -\cot \left ( x \right ) +{\frac{\pi }{2}}-x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.40877, size = 14, normalized size = 1.75 \begin{align*} -x - \frac{1}{\tan \left (x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 2.09818, size = 53, normalized size = 6.62 \begin{align*} -\frac{x \sin \left (2 \, x\right ) + \cos \left (2 \, x\right ) + 1}{\sin \left (2 \, x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.059427, size = 8, normalized size = 1. \begin{align*} - x - \frac{\cos{\left (x \right )}}{\sin{\left (x \right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.06771, size = 24, normalized size = 3. \begin{align*} -x - \frac{1}{2 \, \tan \left (\frac{1}{2} \, x\right )} + \frac{1}{2} \, \tan \left (\frac{1}{2} \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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