Optimal. Leaf size=8 \[ -\frac {1}{5} \sinh \left (\frac {1}{x^5}\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {5321, 2637} \[ -\frac {1}{5} \sinh \left (\frac {1}{x^5}\right ) \]
Antiderivative was successfully verified.
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Rule 2637
Rule 5321
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*}
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Mathematica [A] time = 0.00, size = 8, normalized size = 1.00 \[ -\frac {1}{5} \sinh \left (\frac {1}{x^5}\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.48, size = 6, normalized size = 0.75 \[ -\frac {1}{5} \, \sinh \left (\frac {1}{x^{5}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.12, size = 15, normalized size = 1.88 \[ \frac {1}{10} \, e^{\left (-\frac {1}{x^{5}}\right )} - \frac {1}{10} \, e^{\left (\frac {1}{x^{5}}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 7, normalized size = 0.88 \[ -\frac {\sinh \left (\frac {1}{x^{5}}\right )}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.30, size = 6, normalized size = 0.75 \[ -\frac {1}{5} \, \sinh \left (\frac {1}{x^{5}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.90, size = 15, normalized size = 1.88 \[ \frac {{\mathrm {e}}^{-\frac {1}{x^5}}}{10}-\frac {{\mathrm {e}}^{\frac {1}{x^5}}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 23.18, size = 8, normalized size = 1.00 \[ - \frac {\sinh {\left (\frac {1}{x^{5}} \right )}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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