Optimal. Leaf size=13 \[ -\frac{\sin \left (a+\frac{b}{x}\right )}{b} \]
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Rubi [A] time = 0.0144733, 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 = {3380, 2637} \[ -\frac{\sin \left (a+\frac{b}{x}\right )}{b} \]
Antiderivative was successfully verified.
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Rule 3380
Rule 2637
Rubi steps
\begin{align*} \int \frac{\cos \left (a+\frac{b}{x}\right )}{x^2} \, dx &=-\operatorname{Subst}\left (\int \cos (a+b x) \, dx,x,\frac{1}{x}\right )\\ &=-\frac{\sin \left (a+\frac{b}{x}\right )}{b}\\ \end{align*}
Mathematica [A] time = 0.0028499, size = 13, normalized size = 1. \[ -\frac{\sin \left (a+\frac{b}{x}\right )}{b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.026, size = 14, normalized size = 1.1 \begin{align*} -{\frac{1}{b}\sin \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 = 1.055, size = 18, normalized size = 1.38 \begin{align*} -\frac{\sin \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 = 1.51144, size = 28, normalized size = 2.15 \begin{align*} -\frac{\sin \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 = 1.7594, size = 15, normalized size = 1.15 \begin{align*} \begin{cases} - \frac{\sin{\left (a + \frac{b}{x} \right )}}{b} & \text{for}\: b \neq 0 \\- \frac{\cos{\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 = 1.13324, size = 18, normalized size = 1.38 \begin{align*} -\frac{\sin \left (a + \frac{b}{x}\right )}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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