Optimal. Leaf size=4 \[ -\cot (x) \]
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Rubi [A] time = 0.005372, antiderivative size = 4, 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 = {3767, 8} \[ -\cot (x) \]
Antiderivative was successfully verified.
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Rule 3767
Rule 8
Rubi steps
\begin{align*} \int \csc ^2(x) \, dx &=-\operatorname{Subst}(\int 1 \, dx,x,\cot (x))\\ &=-\cot (x)\\ \end{align*}
Mathematica [A] time = 0.0016446, size = 4, normalized size = 1. \[ -\cot (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 5, normalized size = 1.3 \begin{align*} -\cot \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.937823, size = 8, normalized size = 2. \begin{align*} -\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 = 1.84732, size = 22, normalized size = 5.5 \begin{align*} -\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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Sympy [B] time = 0.05926, size = 7, normalized size = 1.75 \begin{align*} - \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 [A] time = 1.08226, size = 8, normalized size = 2. \begin{align*} -\frac{1}{\tan \left (x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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