Optimal. Leaf size=1 \[ x \]
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Rubi [A] time = 0.0123049, antiderivative size = 1, normalized size of antiderivative = 1., 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 = {4381, 8} \[ x \]
Antiderivative was successfully verified.
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Rule 4381
Rule 8
Rubi steps
\begin{align*} \int \frac{1}{\left (\text{sech}^2(x)+\tanh ^2(x)\right )^2} \, dx &=\int 1 \, dx\\ &=x\\ \end{align*}
Mathematica [A] time = 0.0003646, size = 1, normalized size = 1. \[ x \]
Antiderivative was successfully verified.
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Maple [C] time = 0.024, size = 8, normalized size = 8. \begin{align*} 2\,{\it Artanh} \left ( \tanh \left ( x/2 \right ) \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06034, size = 1, normalized size = 1. \begin{align*} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.12061, size = 4, normalized size = 4. \begin{align*} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\left (\tanh ^{2}{\left (x \right )} + \operatorname{sech}^{2}{\left (x \right )}\right )^{2}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15356, size = 1, normalized size = 1. \begin{align*} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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