Integrand size = 12, antiderivative size = 5 \[ \int \left (\cos (x) \log (x)+\frac {\sin (x)}{x}\right ) \, dx=\log (x) \sin (x) \]
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Time = 0.02 (sec) , antiderivative size = 5, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {2717, 2634, 3380} \[ \int \left (\cos (x) \log (x)+\frac {\sin (x)}{x}\right ) \, dx=\log (x) \sin (x) \]
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Rule 2634
Rule 2717
Rule 3380
Rubi steps \begin{align*} \text {integral}& = \int \cos (x) \log (x) \, dx+\int \frac {\sin (x)}{x} \, dx \\ & = \log (x) \sin (x)+\text {Si}(x)-\int \frac {\sin (x)}{x} \, dx \\ & = \log (x) \sin (x) \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 5, normalized size of antiderivative = 1.00 \[ \int \left (\cos (x) \log (x)+\frac {\sin (x)}{x}\right ) \, dx=\log (x) \sin (x) \]
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Time = 1.46 (sec) , antiderivative size = 6, normalized size of antiderivative = 1.20
method | result | size |
risch | \(\ln \left (x \right ) \sin \left (x \right )\) | \(6\) |
parallelrisch | \(\ln \left (x \right ) \sin \left (x \right )\) | \(6\) |
norman | \(\frac {2 \ln \left (x \right ) \tan \left (\frac {x}{2}\right )}{1+\tan ^{2}\left (\frac {x}{2}\right )}\) | \(19\) |
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none
Time = 0.31 (sec) , antiderivative size = 5, normalized size of antiderivative = 1.00 \[ \int \left (\cos (x) \log (x)+\frac {\sin (x)}{x}\right ) \, dx=\log \left (x\right ) \sin \left (x\right ) \]
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Time = 3.92 (sec) , antiderivative size = 5, normalized size of antiderivative = 1.00 \[ \int \left (\cos (x) \log (x)+\frac {\sin (x)}{x}\right ) \, dx=\log {\left (x \right )} \sin {\left (x \right )} \]
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none
Time = 0.25 (sec) , antiderivative size = 5, normalized size of antiderivative = 1.00 \[ \int \left (\cos (x) \log (x)+\frac {\sin (x)}{x}\right ) \, dx=\log \left (x\right ) \sin \left (x\right ) \]
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none
Time = 0.38 (sec) , antiderivative size = 5, normalized size of antiderivative = 1.00 \[ \int \left (\cos (x) \log (x)+\frac {\sin (x)}{x}\right ) \, dx=\log \left (x\right ) \sin \left (x\right ) \]
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Time = 1.50 (sec) , antiderivative size = 5, normalized size of antiderivative = 1.00 \[ \int \left (\cos (x) \log (x)+\frac {\sin (x)}{x}\right ) \, dx=\ln \left (x\right )\,\sin \left (x\right ) \]
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