Optimal. Leaf size=8 \[ -\frac{1}{2} \csc ^2(x) \]
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Rubi [A] time = 0.0130718, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.286, Rules used = {2606, 30} \[ -\frac{1}{2} \csc ^2(x) \]
Antiderivative was successfully verified.
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Rule 2606
Rule 30
Rubi steps
\begin{align*} \int \cot (x) \csc ^2(x) \, dx &=-\operatorname{Subst}(\int x \, dx,x,\csc (x))\\ &=-\frac{1}{2} \csc ^2(x)\\ \end{align*}
Mathematica [A] time = 0.004811, size = 8, normalized size = 1. \[ -\frac{1}{2} \csc ^2(x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 7, normalized size = 0.9 \begin{align*} -{\frac{1}{2\, \left ( \sin \left ( x \right ) \right ) ^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.942057, size = 8, normalized size = 1. \begin{align*} -\frac{1}{2 \, \sin \left (x\right )^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.43484, size = 27, normalized size = 3.38 \begin{align*} \frac{1}{2 \,{\left (\cos \left (x\right )^{2} - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.059657, size = 8, normalized size = 1. \begin{align*} - \frac{1}{2 \sin ^{2}{\left (x \right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08131, size = 14, normalized size = 1.75 \begin{align*} \frac{1}{2 \,{\left (\cos \left (x\right )^{2} - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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