Optimal. Leaf size=1 \[ x \]
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Rubi [A] time = 0.0149549, 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 = {2282, 29} \[ x \]
Antiderivative was successfully verified.
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Rule 2282
Rule 29
Rubi steps
\begin{align*} \int \frac{e^x}{\cosh (x)+\sinh (x)} \, dx &=\operatorname{Subst}\left (\int \frac{1}{x} \, dx,x,e^x\right )\\ &=x\\ \end{align*}
Mathematica [A] time = 0.0012358, size = 1, normalized size = 1. \[ x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.018, size = 2, normalized size = 2. \begin{align*} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.936195, 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 = 1.91013, 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 [B] time = 0.353225, size = 10, normalized size = 10. \begin{align*} \frac{x e^{x}}{\sinh{\left (x \right )} + \cosh{\left (x \right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08285, size = 1, normalized size = 1. \begin{align*} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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