Integrand size = 7, antiderivative size = 15 \[ \int \cos (2 x) \sin (x) \, dx=\frac {\cos (x)}{2}-\frac {1}{6} \cos (3 x) \]
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Time = 0.01 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {4369} \[ \int \cos (2 x) \sin (x) \, dx=\frac {\cos (x)}{2}-\frac {1}{6} \cos (3 x) \]
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Rule 4369
Rubi steps \begin{align*} \text {integral}& = \frac {\cos (x)}{2}-\frac {1}{6} \cos (3 x) \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00 \[ \int \cos (2 x) \sin (x) \, dx=\frac {\cos (x)}{2}-\frac {1}{6} \cos (3 x) \]
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Time = 0.60 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.80
method | result | size |
default | \(\frac {\cos \left (x \right )}{2}-\frac {\cos \left (3 x \right )}{6}\) | \(12\) |
risch | \(\frac {\cos \left (x \right )}{2}-\frac {\cos \left (3 x \right )}{6}\) | \(12\) |
parallelrisch | \(-\frac {1}{3}+\frac {\cos \left (x \right )}{2}-\frac {\cos \left (3 x \right )}{6}\) | \(13\) |
norman | \(\frac {-\frac {2 \tan \left (x \right )^{2}}{3}-\frac {2 \tan \left (\frac {x}{2}\right )^{2}}{3}+\frac {8 \tan \left (\frac {x}{2}\right ) \tan \left (x \right )}{3}}{\left (1+\tan \left (\frac {x}{2}\right )^{2}\right ) \left (1+\tan \left (x \right )^{2}\right )}\) | \(43\) |
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none
Time = 0.24 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.60 \[ \int \cos (2 x) \sin (x) \, dx=-\frac {2}{3} \, \cos \left (x\right )^{3} + \cos \left (x\right ) \]
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Time = 0.13 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.33 \[ \int \cos (2 x) \sin (x) \, dx=\frac {2 \sin {\left (x \right )} \sin {\left (2 x \right )}}{3} + \frac {\cos {\left (x \right )} \cos {\left (2 x \right )}}{3} \]
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none
Time = 0.19 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.73 \[ \int \cos (2 x) \sin (x) \, dx=-\frac {1}{6} \, \cos \left (3 \, x\right ) + \frac {1}{2} \, \cos \left (x\right ) \]
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none
Time = 0.26 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.73 \[ \int \cos (2 x) \sin (x) \, dx=-\frac {1}{6} \, \cos \left (3 \, x\right ) + \frac {1}{2} \, \cos \left (x\right ) \]
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Time = 0.03 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.60 \[ \int \cos (2 x) \sin (x) \, dx=\cos \left (x\right )-\frac {2\,{\cos \left (x\right )}^3}{3} \]
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