Integrand size = 9, antiderivative size = 8 \[ \int \csc (3 x) \sin (6 x) \, dx=\frac {2}{3} \sin (3 x) \]
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Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {4373, 2717} \[ \int \csc (3 x) \sin (6 x) \, dx=\frac {2}{3} \sin (3 x) \]
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Rule 2717
Rule 4373
Rubi steps \begin{align*} \text {integral}& = 2 \int \cos (3 x) \, dx \\ & = \frac {2}{3} \sin (3 x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int \csc (3 x) \sin (6 x) \, dx=\frac {2}{3} \sin (3 x) \]
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Time = 0.29 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.88
method | result | size |
risch | \(\frac {2 \sin \left (3 x \right )}{3}\) | \(7\) |
derivativedivides | \(\frac {2}{3 \csc \left (3 x \right )}\) | \(9\) |
default | \(\frac {2}{3 \csc \left (3 x \right )}\) | \(9\) |
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none
Time = 0.26 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.75 \[ \int \csc (3 x) \sin (6 x) \, dx=\frac {2}{3} \, \sin \left (3 \, x\right ) \]
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Time = 1.27 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.88 \[ \int \csc (3 x) \sin (6 x) \, dx=\frac {2 \sin {\left (3 x \right )}}{3} \]
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none
Time = 0.20 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.75 \[ \int \csc (3 x) \sin (6 x) \, dx=\frac {2}{3} \, \sin \left (3 \, x\right ) \]
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none
Time = 0.28 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.75 \[ \int \csc (3 x) \sin (6 x) \, dx=\frac {2}{3} \, \sin \left (3 \, x\right ) \]
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Time = 0.03 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.75 \[ \int \csc (3 x) \sin (6 x) \, dx=\frac {2\,\sin \left (3\,x\right )}{3} \]
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