Optimal. Leaf size=11 \[ \frac {1}{2} (\sinh (x)+\cosh (x))^2 \]
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Rubi [A] time = 0.04, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {4385} \[ \frac {1}{2} (\sinh (x)+\cosh (x))^2 \]
Antiderivative was successfully verified.
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Rule 4385
Rubi steps
\begin {align*} \int \frac {\cosh (x)+\sinh (x)}{\cosh (x)-\sinh (x)} \, dx &=\frac {1}{2} (\cosh (x)+\sinh (x))^2\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.55 \[ \frac {1}{2} \sinh (2 x)+\frac {1}{2} \cosh (2 x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.53, size = 16, normalized size = 1.45 \[ \frac {\cosh \relax (x) + \sinh \relax (x)}{2 \, {\left (\cosh \relax (x) - \sinh \relax (x)\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.11, size = 6, normalized size = 0.55 \[ \frac {1}{2} \, e^{\left (2 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 17, normalized size = 1.55 \[ \frac {\cosh \relax (x )+\sinh \relax (x )}{2 \cosh \relax (x )-2 \sinh \relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 6, normalized size = 0.55 \[ \frac {1}{2} \, e^{\left (2 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 6, normalized size = 0.55 \[ \frac {{\mathrm {e}}^{2\,x}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.35, size = 8, normalized size = 0.73 \[ \frac {\cosh {\relax (x )}}{- \sinh {\relax (x )} + \cosh {\relax (x )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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