Optimal. Leaf size=6 \[ e^{-\cot (x)} \]
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Rubi [A] time = 0.01, antiderivative size = 6, normalized size of antiderivative = 1.00, 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 2194
Rule 4344
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*}
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Mathematica [A] time = 0.07, size = 6, normalized size = 1.00 \[ e^{-\cot (x)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 9, normalized size = 1.50 \[ e^{\left (-\frac {\cos \relax (x)}{\sin \relax (x)}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \csc \relax (x)^{2} e^{\left (-\cot \relax (x)\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 6, normalized size = 1.00 \[ {\mathrm e}^{-\cot \relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.32, size = 5, normalized size = 0.83 \[ e^{\left (-\cot \relax (x)\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.94, size = 7, normalized size = 1.17 \[ {\mathrm {e}}^{-\frac {1}{\mathrm {tan}\relax (x)}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 18.87, size = 5, normalized size = 0.83 \[ e^{- \cot {\relax (x )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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