Optimal. Leaf size=8 \[ \frac{2 \cosh ^3(x)}{3} \]
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Rubi [A] time = 0.0105073, antiderivative size = 15, normalized size of antiderivative = 1.88, 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} \[ \frac{\cosh (x)}{2}+\frac{1}{6} \cosh (3 x) \]
Antiderivative was successfully verified.
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Rule 4284
Rubi steps
\begin{align*} \int \cosh (x) \sinh (2 x) \, dx &=\frac{\cosh (x)}{2}+\frac{1}{6} \cosh (3 x)\\ \end{align*}
Mathematica [A] time = 0.0052221, size = 15, normalized size = 1.88 \[ \frac{\cosh (x)}{2}+\frac{1}{6} \cosh (3 x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 7, normalized size = 0.9 \begin{align*}{\frac{2\, \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 [B] time = 1.00849, size = 36, normalized size = 4.5 \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 [B] time = 1.98672, size = 72, normalized size = 9. \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 [B] time = 0.647082, size = 20, normalized size = 2.5 \begin{align*} - \frac{\sinh{\left (x \right )} \sinh{\left (2 x \right )}}{3} + \frac{2 \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 = 1.22339, size = 34, normalized size = 4.25 \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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