Integrand size = 6, antiderivative size = 6 \[ \int (1+2 \sin (x)) \, dx=x-2 \cos (x) \]
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Time = 0.00 (sec) , antiderivative size = 6, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {2718} \[ \int (1+2 \sin (x)) \, dx=x-2 \cos (x) \]
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Rule 2718
Rubi steps \begin{align*} \text {integral}& = x+2 \int \sin (x) \, dx \\ & = x-2 \cos (x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 6, normalized size of antiderivative = 1.00 \[ \int (1+2 \sin (x)) \, dx=x-2 \cos (x) \]
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Time = 0.04 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.17
method | result | size |
default | \(x -2 \cos \left (x \right )\) | \(7\) |
risch | \(x -2 \cos \left (x \right )\) | \(7\) |
parts | \(x -2 \cos \left (x \right )\) | \(7\) |
parallelrisch | \(-2-2 \cos \left (x \right )+x\) | \(8\) |
norman | \(\frac {x +x \tan \left (\frac {x}{2}\right )^{2}-4}{1+\tan \left (\frac {x}{2}\right )^{2}}\) | \(23\) |
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none
Time = 0.25 (sec) , antiderivative size = 6, normalized size of antiderivative = 1.00 \[ \int (1+2 \sin (x)) \, dx=x - 2 \, \cos \left (x\right ) \]
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Time = 0.02 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.83 \[ \int (1+2 \sin (x)) \, dx=x - 2 \cos {\left (x \right )} \]
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none
Time = 0.21 (sec) , antiderivative size = 6, normalized size of antiderivative = 1.00 \[ \int (1+2 \sin (x)) \, dx=x - 2 \, \cos \left (x\right ) \]
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none
Time = 0.27 (sec) , antiderivative size = 6, normalized size of antiderivative = 1.00 \[ \int (1+2 \sin (x)) \, dx=x - 2 \, \cos \left (x\right ) \]
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Time = 18.42 (sec) , antiderivative size = 6, normalized size of antiderivative = 1.00 \[ \int (1+2 \sin (x)) \, dx=x-2\,\cos \left (x\right ) \]
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