Optimal. Leaf size=17 \[ \frac{1}{4} \cosh (2 x)+\frac{1}{8} \cosh (4 x) \]
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Rubi [A] time = 0.0106027, 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} \[ \frac{1}{4} \cosh (2 x)+\frac{1}{8} \cosh (4 x) \]
Antiderivative was successfully verified.
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Rule 4284
Rubi steps
\begin{align*} \int \cosh (x) \sinh (3 x) \, dx &=\frac{1}{4} \cosh (2 x)+\frac{1}{8} \cosh (4 x)\\ \end{align*}
Mathematica [A] time = 0.0069289, size = 17, normalized size = 1. \[ \frac{\cosh ^2(x)}{2}+\frac{1}{8} \cosh (4 x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.014, size = 12, normalized size = 0.7 \begin{align*} \left ( \cosh \left ( x \right ) \right ) ^{4}-{\frac{ \left ( \cosh \left ( x \right ) \right ) ^{2}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04745, 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 [B] time = 2.1121, size = 109, normalized size = 6.41 \begin{align*} \frac{1}{8} \, \cosh \left (x\right )^{4} + \frac{1}{8} \, \sinh \left (x\right )^{4} + \frac{1}{4} \,{\left (3 \, \cosh \left (x\right )^{2} + 1\right )} \sinh \left (x\right )^{2} + \frac{1}{4} \, \cosh \left (x\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.558174, size = 20, normalized size = 1.18 \begin{align*} - \frac{\sinh{\left (x \right )} \sinh{\left (3 x \right )}}{8} + \frac{3 \cosh{\left (x \right )} \cosh{\left (3 x \right )}}{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19394, size = 35, normalized size = 2.06 \begin{align*} \frac{1}{16} \,{\left (e^{\left (2 \, x\right )} + e^{\left (-2 \, x\right )}\right )}^{2} + \frac{1}{8} \, e^{\left (2 \, 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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