Optimal. Leaf size=17 \[ \frac{1}{4} \sinh (2 x)+\frac{1}{8} \sinh (4 x) \]
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Rubi [A] time = 0.0087817, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {4283} \[ \frac{1}{4} \sinh (2 x)+\frac{1}{8} \sinh (4 x) \]
Antiderivative was successfully verified.
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Rule 4283
Rubi steps
\begin{align*} \int \cosh (x) \cosh (3 x) \, dx &=\frac{1}{4} \sinh (2 x)+\frac{1}{8} \sinh (4 x)\\ \end{align*}
Mathematica [A] time = 0.0056586, size = 17, normalized size = 1. \[ \frac{1}{4} \sinh (2 x)+\frac{1}{8} \sinh (4 x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.018, size = 14, normalized size = 0.8 \begin{align*}{\frac{\sinh \left ( 2\,x \right ) }{4}}+{\frac{\sinh \left ( 4\,x \right ) }{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0541, size = 36, normalized size = 2.12 \begin{align*} \frac{1}{16} \,{\left (2 \, e^{\left (-2 \, x\right )} + 1\right )} e^{\left (4 \, x\right )} - \frac{1}{8} \, e^{\left (-2 \, x\right )} - \frac{1}{16} \, e^{\left (-4 \, x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.13975, size = 80, normalized size = 4.71 \begin{align*} \frac{1}{2} \, \cosh \left (x\right ) \sinh \left (x\right )^{3} + \frac{1}{2} \,{\left (\cosh \left (x\right )^{3} + \cosh \left (x\right )\right )} \sinh \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.571234, size = 20, normalized size = 1.18 \begin{align*} - \frac{\sinh{\left (x \right )} \cosh{\left (3 x \right )}}{8} + \frac{3 \sinh{\left (3 x \right )} \cosh{\left (x \right )}}{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17635, size = 36, normalized size = 2.12 \begin{align*} -\frac{1}{16} \,{\left (2 \, e^{\left (2 \, x\right )} + 1\right )} e^{\left (-4 \, x\right )} + \frac{1}{16} \, e^{\left (4 \, x\right )} + \frac{1}{8} \, e^{\left (2 \, x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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