Optimal. Leaf size=13 \[ -\frac{\sinh \left (a+\frac{b}{x}\right )}{b} \]
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Rubi [A] time = 0.0153976, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167, Rules used = {5321, 2637} \[ -\frac{\sinh \left (a+\frac{b}{x}\right )}{b} \]
Antiderivative was successfully verified.
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Rule 5321
Rule 2637
Rubi steps
\begin{align*} \int \frac{\cosh \left (a+\frac{b}{x}\right )}{x^2} \, dx &=-\operatorname{Subst}\left (\int \cosh (a+b x) \, dx,x,\frac{1}{x}\right )\\ &=-\frac{\sinh \left (a+\frac{b}{x}\right )}{b}\\ \end{align*}
Mathematica [A] time = 0.0040761, size = 13, normalized size = 1. \[ -\frac{\sinh \left (a+\frac{b}{x}\right )}{b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 14, normalized size = 1.1 \begin{align*} -{\frac{1}{b}\sinh \left ( a+{\frac{b}{x}} \right ) } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.11802, size = 18, normalized size = 1.38 \begin{align*} -\frac{\sinh \left (a + \frac{b}{x}\right )}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.68785, size = 30, normalized size = 2.31 \begin{align*} -\frac{\sinh \left (\frac{a x + b}{x}\right )}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.42341, size = 15, normalized size = 1.15 \begin{align*} \begin{cases} - \frac{\sinh{\left (a + \frac{b}{x} \right )}}{b} & \text{for}\: b \neq 0 \\- \frac{\cosh{\left (a \right )}}{x} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.26006, size = 36, normalized size = 2.77 \begin{align*} -\frac{e^{\left (a + \frac{b}{x}\right )} - e^{\left (-a - \frac{b}{x}\right )}}{2 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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