Optimal. Leaf size=10 \[ -\frac{1}{2} \sin ^2\left (\frac{1}{x}\right ) \]
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Rubi [A] time = 0.0123809, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083, Rules used = {3441} \[ -\frac{1}{2} \sin ^2\left (\frac{1}{x}\right ) \]
Antiderivative was successfully verified.
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Rule 3441
Rubi steps
\begin{align*} \int \frac{\cos \left (\frac{1}{x}\right ) \sin \left (\frac{1}{x}\right )}{x^2} \, dx &=-\frac{1}{2} \sin ^2\left (\frac{1}{x}\right )\\ \end{align*}
Mathematica [A] time = 0.0053399, size = 10, normalized size = 1. \[ \frac{1}{2} \cos ^2\left (\frac{1}{x}\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 9, normalized size = 0.9 \begin{align*}{\frac{ \left ( \cos \left ({x}^{-1} \right ) \right ) ^{2}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.949932, size = 11, normalized size = 1.1 \begin{align*} \frac{1}{2} \, \cos \left (\frac{1}{x}\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.19054, size = 22, normalized size = 2.2 \begin{align*} \frac{1}{2} \, \cos \left (\frac{1}{x}\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.74315, size = 31, normalized size = 3.1 \begin{align*} - \frac{2 \tan ^{2}{\left (\frac{1}{2 x} \right )}}{\tan ^{4}{\left (\frac{1}{2 x} \right )} + 2 \tan ^{2}{\left (\frac{1}{2 x} \right )} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06668, size = 11, normalized size = 1.1 \begin{align*} \frac{1}{2} \, \cos \left (\frac{1}{x}\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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