Optimal. Leaf size=10 \[ -\frac {1}{2} \sin ^2\left (\frac {1}{x}\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 10, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, size = 10, normalized size = 1.00 \[ \frac {1}{2} \cos ^2\left (\frac {1}{x}\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 8, normalized size = 0.80 \[ \frac {1}{2} \, \cos \left (\frac {1}{x}\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 8, normalized size = 0.80 \[ \frac {1}{2} \, \cos \left (\frac {1}{x}\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 9, normalized size = 0.90 \[ \frac {\left (\cos ^{2}\left (\frac {1}{x}\right )\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.33, size = 8, normalized size = 0.80 \[ \frac {1}{2} \, \cos \left (\frac {1}{x}\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.92, size = 8, normalized size = 0.80 \[ \frac {{\cos \left (\frac {1}{x}\right )}^2}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.28, size = 31, normalized size = 3.10 \[ - \frac {2 \tan ^{2}{\left (\frac {1}{2 x} \right )}}{\tan ^{4}{\left (\frac {1}{2 x} \right )} + 2 \tan ^{2}{\left (\frac {1}{2 x} \right )} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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