Integrand size = 8, antiderivative size = 4 \[ \int \frac {\sin \left (\frac {1}{x}\right )}{x^2} \, dx=\cos \left (\frac {1}{x}\right ) \]
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Time = 0.01 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {3460, 2718} \[ \int \frac {\sin \left (\frac {1}{x}\right )}{x^2} \, dx=\cos \left (\frac {1}{x}\right ) \]
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Rule 2718
Rule 3460
Rubi steps \begin{align*} \text {integral}& = -\text {Subst}\left (\int \sin (x) \, dx,x,\frac {1}{x}\right ) \\ & = \cos \left (\frac {1}{x}\right ) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.00 \[ \int \frac {\sin \left (\frac {1}{x}\right )}{x^2} \, dx=\cos \left (\frac {1}{x}\right ) \]
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Time = 0.05 (sec) , antiderivative size = 5, normalized size of antiderivative = 1.25
method | result | size |
derivativedivides | \(\cos \left (\frac {1}{x}\right )\) | \(5\) |
default | \(\cos \left (\frac {1}{x}\right )\) | \(5\) |
risch | \(\cos \left (\frac {1}{x}\right )\) | \(5\) |
parallelrisch | \(1+\cos \left (\frac {1}{x}\right )\) | \(7\) |
norman | \(\frac {2}{1+\tan ^{2}\left (\frac {1}{2 x}\right )}\) | \(15\) |
meijerg | \(-\sqrt {\pi }\, \left (\frac {1}{\sqrt {\pi }}-\frac {\cos \left (\frac {1}{x}\right )}{\sqrt {\pi }}\right )\) | \(19\) |
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none
Time = 0.23 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.00 \[ \int \frac {\sin \left (\frac {1}{x}\right )}{x^2} \, dx=\cos \left (\frac {1}{x}\right ) \]
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Time = 0.18 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.75 \[ \int \frac {\sin \left (\frac {1}{x}\right )}{x^2} \, dx=\cos {\left (\frac {1}{x} \right )} \]
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none
Time = 0.21 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.00 \[ \int \frac {\sin \left (\frac {1}{x}\right )}{x^2} \, dx=\cos \left (\frac {1}{x}\right ) \]
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none
Time = 0.27 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.00 \[ \int \frac {\sin \left (\frac {1}{x}\right )}{x^2} \, dx=\cos \left (\frac {1}{x}\right ) \]
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Time = 0.10 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.00 \[ \int \frac {\sin \left (\frac {1}{x}\right )}{x^2} \, dx=\cos \left (\frac {1}{x}\right ) \]
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