Optimal. Leaf size=17 \[ \frac{1}{6} \cosh (3 x)+\frac{1}{10} \cosh (5 x) \]
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Rubi [A] time = 0.0108065, 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 = {4284} \[ \frac{1}{6} \cosh (3 x)+\frac{1}{10} \cosh (5 x) \]
Antiderivative was successfully verified.
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Rule 4284
Rubi steps
\begin{align*} \int \cosh (x) \sinh (4 x) \, dx &=\frac{1}{6} \cosh (3 x)+\frac{1}{10} \cosh (5 x)\\ \end{align*}
Mathematica [A] time = 0.0059692, size = 17, normalized size = 1. \[ \frac{1}{6} \cosh (3 x)+\frac{1}{10} \cosh (5 x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.011, size = 14, normalized size = 0.8 \begin{align*}{\frac{8\, \left ( \cosh \left ( x \right ) \right ) ^{5}}{5}}-{\frac{4\, \left ( \cosh \left ( x \right ) \right ) ^{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03567, size = 36, normalized size = 2.12 \begin{align*} \frac{1}{60} \,{\left (5 \, e^{\left (-2 \, x\right )} + 3\right )} e^{\left (5 \, x\right )} + \frac{1}{12} \, e^{\left (-3 \, x\right )} + \frac{1}{20} \, e^{\left (-5 \, x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 2.0702, size = 130, normalized size = 7.65 \begin{align*} \frac{1}{10} \, \cosh \left (x\right )^{5} + \frac{1}{2} \, \cosh \left (x\right ) \sinh \left (x\right )^{4} + \frac{1}{6} \, \cosh \left (x\right )^{3} + \frac{1}{2} \,{\left (2 \, \cosh \left (x\right )^{3} + \cosh \left (x\right )\right )} \sinh \left (x\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.586667, size = 20, normalized size = 1.18 \begin{align*} - \frac{\sinh{\left (x \right )} \sinh{\left (4 x \right )}}{15} + \frac{4 \cosh{\left (x \right )} \cosh{\left (4 x \right )}}{15} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15576, size = 36, normalized size = 2.12 \begin{align*} \frac{1}{60} \,{\left (5 \, e^{\left (2 \, x\right )} + 3\right )} e^{\left (-5 \, x\right )} + \frac{1}{20} \, e^{\left (5 \, x\right )} + \frac{1}{12} \, e^{\left (3 \, x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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