Optimal. Leaf size=2 \[ \cosh (x) \]
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Rubi [A] time = 0.0029761, antiderivative size = 2, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 2, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5, Rules used = {2638} \[ \cosh (x) \]
Antiderivative was successfully verified.
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Rule 2638
Rubi steps
\begin{align*} \int \sinh (x) \, dx &=\cosh (x)\\ \end{align*}
Mathematica [A] time = 0.0010051, size = 2, normalized size = 1. \[ \cosh (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 3, normalized size = 1.5 \begin{align*} \cosh \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.926615, size = 3, normalized size = 1.5 \begin{align*} \cosh \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.99209, size = 12, normalized size = 6. \begin{align*} \cosh \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.110663, size = 2, normalized size = 1. \begin{align*} \cosh{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.10054, size = 15, normalized size = 7.5 \begin{align*} \frac{1}{2} \, e^{\left (-x\right )} + \frac{1}{2} \, e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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