Integrand size = 6, antiderivative size = 5 \[ \int \frac {\sin (a)}{x} \, dx=\log (x) \sin (a) \]
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Time = 0.01 (sec) , antiderivative size = 5, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {12, 29} \[ \int \frac {\sin (a)}{x} \, dx=\sin (a) \log (x) \]
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Rule 12
Rule 29
Rubi steps \begin{align*} \text {integral}& = \sin (a) \int \frac {1}{x} \, dx \\ & = \log (x) \sin (a) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 1.00 \[ \int \frac {\sin (a)}{x} \, dx=\log (x) \sin (a) \]
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Time = 0.04 (sec) , antiderivative size = 6, normalized size of antiderivative = 1.20
method | result | size |
default | \(\ln \left (x \right ) \sin \left (a \right )\) | \(6\) |
norman | \(\ln \left (x \right ) \sin \left (a \right )\) | \(6\) |
risch | \(\ln \left (x \right ) \sin \left (a \right )\) | \(6\) |
parallelrisch | \(\ln \left (x \right ) \sin \left (a \right )\) | \(6\) |
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none
Time = 0.23 (sec) , antiderivative size = 5, normalized size of antiderivative = 1.00 \[ \int \frac {\sin (a)}{x} \, dx=\log \left (x\right ) \sin \left (a\right ) \]
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Time = 0.02 (sec) , antiderivative size = 5, normalized size of antiderivative = 1.00 \[ \int \frac {\sin (a)}{x} \, dx=\log {\left (x \right )} \sin {\left (a \right )} \]
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none
Time = 0.19 (sec) , antiderivative size = 5, normalized size of antiderivative = 1.00 \[ \int \frac {\sin (a)}{x} \, dx=\log \left (x\right ) \sin \left (a\right ) \]
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none
Time = 0.28 (sec) , antiderivative size = 6, normalized size of antiderivative = 1.20 \[ \int \frac {\sin (a)}{x} \, dx=\log \left ({\left | x \right |}\right ) \sin \left (a\right ) \]
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Time = 26.23 (sec) , antiderivative size = 5, normalized size of antiderivative = 1.00 \[ \int \frac {\sin (a)}{x} \, dx=\sin \left (a\right )\,\ln \left (x\right ) \]
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