Optimal. Leaf size=4 \[ -\csc (x) \]
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Rubi [A] time = 0.0078946, antiderivative size = 4, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 5, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.4, Rules used = {2606, 8} \[ -\csc (x) \]
Antiderivative was successfully verified.
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Rule 2606
Rule 8
Rubi steps
\begin{align*} \int \cot (x) \csc (x) \, dx &=-\operatorname{Subst}(\int 1 \, dx,x,\csc (x))\\ &=-\csc (x)\\ \end{align*}
Mathematica [A] time = 0.0015108, size = 4, normalized size = 1. \[ -\csc (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 5, normalized size = 1.3 \begin{align*} -\csc \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.91894, size = 8, normalized size = 2. \begin{align*} -\frac{1}{\sin \left (x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.8661, size = 15, normalized size = 3.75 \begin{align*} -\frac{1}{\sin \left (x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.062908, size = 5, normalized size = 1.25 \begin{align*} - \frac{1}{\sin{\left (x \right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.0601, size = 8, normalized size = 2. \begin{align*} -\frac{1}{\sin \left (x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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