Optimal. Leaf size=10 \[ -\frac {3}{4} \text {csch}^{\frac {4}{3}}(x) \]
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Rubi [A] time = 0.03, antiderivative size = 10, normalized size of antiderivative = 1.00, 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 30
Rule 2621
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*}
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Mathematica [A] time = 0.01, size = 10, normalized size = 1.00 \[ -\frac {3}{4} \text {csch}^{\frac {4}{3}}(x) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.46, size = 54, normalized size = 5.40 \[ -\frac {3 \cdot 2^{\frac {1}{3}} \left (\frac {\cosh \relax (x) + \sinh \relax (x)}{\cosh \relax (x)^{2} + 2 \, \cosh \relax (x) \sinh \relax (x) + \sinh \relax (x)^{2} - 1}\right )^{\frac {1}{3}} {\left (\cosh \relax (x) + \sinh \relax (x)\right )}}{2 \, {\left (\cosh \relax (x)^{2} + 2 \, \cosh \relax (x) \sinh \relax (x) + \sinh \relax (x)^{2} - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.13, size = 17, normalized size = 1.70 \[ -\frac {3 \cdot 2^{\frac {1}{3}} e^{\left (\frac {4}{3} \, x\right )}}{2 \, {\left (e^{\left (2 \, x\right )} - 1\right )}^{\frac {4}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 7, normalized size = 0.70 \[ -\frac {3 \mathrm {csch}\relax (x )^{\frac {4}{3}}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \cosh \relax (x) \operatorname {csch}\relax (x)^{\frac {7}{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.46, size = 31, normalized size = 3.10 \[ -\frac {3\,{\mathrm {e}}^x\,{\left (-\frac {1}{\frac {{\mathrm {e}}^{-x}}{2}-\frac {{\mathrm {e}}^x}{2}}\right )}^{1/3}}{2\,\left ({\mathrm {e}}^{2\,x}-1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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