Optimal. Leaf size=10 \[ -\frac{3}{4} \text{csch}^{\frac{4}{3}}(x) \]
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Rubi [A] time = 0.0259891, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222, Rules used = {2621, 30} \[ -\frac{3}{4} \text{csch}^{\frac{4}{3}}(x) \]
Antiderivative was successfully verified.
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Rule 2621
Rule 30
Rubi steps
\begin{align*} \int \cosh (x) \text{csch}^{\frac{7}{3}}(x) \, dx &=-\operatorname{Subst}\left (\int \sqrt [3]{x} \, dx,x,\text{csch}(x)\right )\\ &=-\frac{3}{4} \text{csch}^{\frac{4}{3}}(x)\\ \end{align*}
Mathematica [A] time = 0.0077568, size = 10, normalized size = 1. \[ -\frac{3}{4} \text{csch}^{\frac{4}{3}}(x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 7, normalized size = 0.7 \begin{align*} -{\frac{3}{4} \left ({\rm csch} \left (x\right ) \right ) ^{{\frac{4}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \cosh \left (x\right ) \operatorname{csch}\left (x\right )^{\frac{7}{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.82942, size = 213, normalized size = 21.3 \begin{align*} -\frac{3 \cdot 2^{\frac{1}{3}} \left (\frac{\cosh \left (x\right ) + \sinh \left (x\right )}{\cosh \left (x\right )^{2} + 2 \, \cosh \left (x\right ) \sinh \left (x\right ) + \sinh \left (x\right )^{2} - 1}\right )^{\frac{1}{3}}{\left (\cosh \left (x\right ) + \sinh \left (x\right )\right )}}{2 \,{\left (\cosh \left (x\right )^{2} + 2 \, \cosh \left (x\right ) \sinh \left (x\right ) + \sinh \left (x\right )^{2} - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \cosh \left (x\right ) \operatorname{csch}\left (x\right )^{\frac{7}{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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