Optimal. Leaf size=12 \[ \frac {\cos \left (a+\frac {b}{x}\right )}{b} \]
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Rubi [A] time = 0.01, antiderivative size = 12, normalized size of antiderivative = 1.00, 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 = {3379, 2638} \[ \frac {\cos \left (a+\frac {b}{x}\right )}{b} \]
Antiderivative was successfully verified.
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Rule 2638
Rule 3379
Rubi steps
\begin {align*} \int \frac {\sin \left (a+\frac {b}{x}\right )}{x^2} \, dx &=-\operatorname {Subst}\left (\int \sin (a+b x) \, dx,x,\frac {1}{x}\right )\\ &=\frac {\cos \left (a+\frac {b}{x}\right )}{b}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 12, normalized size = 1.00 \[ \frac {\cos \left (a+\frac {b}{x}\right )}{b} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.82, size = 14, normalized size = 1.17 \[ \frac {\cos \left (\frac {a x + b}{x}\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.43, size = 14, normalized size = 1.17 \[ \frac {\cos \left (\frac {a x + b}{x}\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 13, normalized size = 1.08 \[ \frac {\cos \left (a +\frac {b}{x}\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.30, size = 12, normalized size = 1.00 \[ \frac {\cos \left (a + \frac {b}{x}\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.53, size = 12, normalized size = 1.00 \[ \frac {\cos \left (a+\frac {b}{x}\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.21, size = 14, normalized size = 1.17 \[ \begin {cases} \frac {\cos {\left (a + \frac {b}{x} \right )}}{b} & \text {for}\: b \neq 0 \\- \frac {\sin {\relax (a )}}{x} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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