Optimal. Leaf size=17 \[ \frac {1}{4} \sinh (2 x)+\frac {1}{8} \sinh (4 x) \]
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Rubi [A] time = 0.01, antiderivative size = 17, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 1.00 \[ \frac {1}{4} \sinh (2 x)+\frac {1}{8} \sinh (4 x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 20, normalized size = 1.18 \[ \frac {1}{2} \, \cosh \relax (x) \sinh \relax (x)^{3} + \frac {1}{2} \, {\left (\cosh \relax (x)^{3} + \cosh \relax (x)\right )} \sinh \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.11, size = 27, normalized size = 1.59 \[ -\frac {1}{16} \, {\left (2 \, e^{\left (2 \, x\right )} + 1\right )} e^{\left (-4 \, x\right )} + \frac {1}{16} \, e^{\left (4 \, x\right )} + \frac {1}{8} \, e^{\left (2 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.21, size = 14, normalized size = 0.82 \[ \frac {\sinh \left (2 x \right )}{4}+\frac {\sinh \left (4 x \right )}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.33, size = 27, normalized size = 1.59 \[ \frac {1}{16} \, {\left (2 \, e^{\left (-2 \, x\right )} + 1\right )} e^{\left (4 \, x\right )} - \frac {1}{8} \, e^{\left (-2 \, x\right )} - \frac {1}{16} \, e^{\left (-4 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.45, size = 20, normalized size = 1.18 \[ \frac {{\mathrm {e}}^{-4\,x}\,\left ({\mathrm {e}}^{2\,x}-1\right )\,{\left ({\mathrm {e}}^{2\,x}+1\right )}^3}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.41, size = 20, normalized size = 1.18 \[ - \frac {\sinh {\relax (x )} \cosh {\left (3 x \right )}}{8} + \frac {3 \sinh {\left (3 x \right )} \cosh {\relax (x )}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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