Optimal. Leaf size=4 \[ \cos \left (\frac{1}{x}\right ) \]
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Rubi [A] time = 0.0082888, antiderivative size = 4, 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 = {3379, 2638} \[ \cos \left (\frac{1}{x}\right ) \]
Antiderivative was successfully verified.
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Rule 3379
Rule 2638
Rubi steps
\begin{align*} \int \frac{\sin \left (\frac{1}{x}\right )}{x^2} \, dx &=-\operatorname{Subst}\left (\int \sin (x) \, dx,x,\frac{1}{x}\right )\\ &=\cos \left (\frac{1}{x}\right )\\ \end{align*}
Mathematica [A] time = 0.0075307, size = 4, normalized size = 1. \[ \cos \left (\frac{1}{x}\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 5, normalized size = 1.3 \begin{align*} \cos \left ({x}^{-1} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.979889, size = 5, normalized size = 1.25 \begin{align*} \cos \left (\frac{1}{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.44653, size = 14, normalized size = 3.5 \begin{align*} \cos \left (\frac{1}{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.654624, size = 3, normalized size = 0.75 \begin{align*} \cos{\left (\frac{1}{x} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08327, size = 5, normalized size = 1.25 \begin{align*} \cos \left (\frac{1}{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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