Optimal. Leaf size=15 \[ \frac{1}{6} \cosh (3 x)-\frac{\cosh (x)}{2} \]
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Rubi [A] time = 0.009962, antiderivative size = 15, 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} \[ \frac{1}{6} \cosh (3 x)-\frac{\cosh (x)}{2} \]
Antiderivative was successfully verified.
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Rule 4284
Rubi steps
\begin{align*} \int \cosh (2 x) \sinh (x) \, dx &=-\frac{\cosh (x)}{2}+\frac{1}{6} \cosh (3 x)\\ \end{align*}
Mathematica [A] time = 0.0050589, size = 15, normalized size = 1. \[ \frac{1}{6} \cosh (3 x)-\frac{\cosh (x)}{2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.01, size = 12, normalized size = 0.8 \begin{align*} -{\frac{\cosh \left ( x \right ) }{2}}+{\frac{\cosh \left ( 3\,x \right ) }{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.09112, size = 36, normalized size = 2.4 \begin{align*} -\frac{1}{12} \,{\left (3 \, e^{\left (-2 \, x\right )} - 1\right )} e^{\left (3 \, x\right )} - \frac{1}{4} \, e^{\left (-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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Fricas [A] time = 2.07606, size = 72, normalized size = 4.8 \begin{align*} \frac{1}{6} \, \cosh \left (x\right )^{3} + \frac{1}{2} \, \cosh \left (x\right ) \sinh \left (x\right )^{2} - \frac{1}{2} \, \cosh \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.608357, size = 20, normalized size = 1.33 \begin{align*} \frac{2 \sinh{\left (x \right )} \sinh{\left (2 x \right )}}{3} - \frac{\cosh{\left (x \right )} \cosh{\left (2 x \right )}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.1749, size = 34, normalized size = 2.27 \begin{align*} -\frac{1}{12} \,{\left (3 \, e^{\left (2 \, x\right )} - 1\right )} e^{\left (-3 \, x\right )} + \frac{1}{12} \, e^{\left (3 \, x\right )} - \frac{1}{4} \, e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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