Optimal. Leaf size=3 \[ -x \]
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Rubi [A] time = 0.0131694, antiderivative size = 3, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {4382, 8} \[ -x \]
Antiderivative was successfully verified.
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Rule 4382
Rule 8
Rubi steps
\begin{align*} \int \frac{1}{\left (\cot ^2(x)-\csc ^2(x)\right )^3} \, dx &=-\int 1 \, dx\\ &=-x\\ \end{align*}
Mathematica [A] time = 0.0005598, size = 3, normalized size = 1. \[ -x \]
Antiderivative was successfully verified.
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Maple [C] time = 0.029, size = 6, normalized size = 2. \begin{align*} -\arctan \left ( \tan \left ( x \right ) \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.48669, size = 4, normalized size = 1.33 \begin{align*} -x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.48543, size = 5, normalized size = 1.67 \begin{align*} -x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12165, size = 4, normalized size = 1.33 \begin{align*} -x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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