Optimal. Leaf size=6 \[ e^{-\cot (x)} \]
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Rubi [A] time = 0.0147822, antiderivative size = 6, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182, Rules used = {4344, 2194} \[ e^{-\cot (x)} \]
Antiderivative was successfully verified.
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Rule 4344
Rule 2194
Rubi steps
\begin{align*} \int e^{-\cot (x)} \csc ^2(x) \, dx &=-\operatorname{Subst}\left (\int e^{-x} \, dx,x,\cot (x)\right )\\ &=e^{-\cot (x)}\\ \end{align*}
Mathematica [A] time = 0.0762972, size = 6, normalized size = 1. \[ e^{-\cot (x)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.011, size = 6, normalized size = 1. \begin{align*} \left ({{\rm e}^{\cot \left ( x \right ) }} \right ) ^{-1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.978347, size = 7, normalized size = 1.17 \begin{align*} e^{\left (-\cot \left (x\right )\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.23891, size = 27, normalized size = 4.5 \begin{align*} e^{\left (-\frac{\cos \left (x\right )}{\sin \left (x\right )}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 115.646, size = 5, normalized size = 0.83 \begin{align*} e^{- \cot{\left (x \right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \csc \left (x\right )^{2} e^{\left (-\cot \left (x\right )\right )}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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