Optimal. Leaf size=8 \[ -\frac{1}{5} \sinh \left (\frac{1}{x^5}\right ) \]
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Rubi [A] time = 0.0120885, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25, Rules used = {5321, 2637} \[ -\frac{1}{5} \sinh \left (\frac{1}{x^5}\right ) \]
Antiderivative was successfully verified.
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Rule 5321
Rule 2637
Rubi steps
\begin{align*} \int \frac{\cosh \left (\frac{1}{x^5}\right )}{x^6} \, dx &=-\left (\frac{1}{5} \operatorname{Subst}\left (\int \cosh (x) \, dx,x,\frac{1}{x^5}\right )\right )\\ &=-\frac{1}{5} \sinh \left (\frac{1}{x^5}\right )\\ \end{align*}
Mathematica [A] time = 0.0044277, size = 8, normalized size = 1. \[ -\frac{1}{5} \sinh \left (\frac{1}{x^5}\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 7, normalized size = 0.9 \begin{align*} -{\frac{\sinh \left ({x}^{-5} \right ) }{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.14956, size = 8, normalized size = 1. \begin{align*} -\frac{1}{5} \, \sinh \left (\frac{1}{x^{5}}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.67049, size = 26, normalized size = 3.25 \begin{align*} -\frac{1}{5} \, \sinh \left (\frac{1}{x^{5}}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 43.3938, size = 8, normalized size = 1. \begin{align*} - \frac{\sinh{\left (\frac{1}{x^{5}} \right )}}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.2444, size = 20, normalized size = 2.5 \begin{align*} \frac{1}{10} \, e^{\left (-\frac{1}{x^{5}}\right )} - \frac{1}{10} \, e^{\left (\frac{1}{x^{5}}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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