Optimal. Leaf size=9 \[ \frac{e^{2 x}}{2} \]
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Rubi [A] time = 0.016691, antiderivative size = 9, 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 = {2282, 30} \[ \frac{e^{2 x}}{2} \]
Antiderivative was successfully verified.
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Rule 2282
Rule 30
Rubi steps
\begin{align*} \int \frac{e^x}{\cosh (x)-\sinh (x)} \, dx &=\operatorname{Subst}\left (\int x \, dx,x,e^x\right )\\ &=\frac{e^{2 x}}{2}\\ \end{align*}
Mathematica [A] time = 0.0030923, size = 9, normalized size = 1. \[ \frac{e^{2 x}}{2} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.002, size = 14, normalized size = 1.6 \begin{align*} -{\frac{{{\rm e}^{x}}}{-2\,\cosh \left ( x \right ) +2\,\sinh \left ( x \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.943977, size = 8, normalized size = 0.89 \begin{align*} \frac{1}{2} \, e^{\left (2 \, x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 2.02849, size = 61, normalized size = 6.78 \begin{align*} \frac{\cosh \left (x\right ) + \sinh \left (x\right )}{2 \,{\left (\cosh \left (x\right ) - \sinh \left (x\right )\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.380086, size = 12, normalized size = 1.33 \begin{align*} \frac{e^{x}}{- 2 \sinh{\left (x \right )} + 2 \cosh{\left (x \right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09636, size = 8, normalized size = 0.89 \begin{align*} \frac{1}{2} \, e^{\left (2 \, x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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