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Answer
$$ \displaystyle\int {\left(\sin\left(2\right){\cdot}x\right)}^{12}{\cdot}\cos\left(2\right){\cdot}x\, \mathrm d x = {{{\it cos}_{2}\,{\it sin}_{2}^{12}\,x^{14}}\over{14}} $$
Explanation
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