Mathematics

Evaluate the following integral:
$$\int { { e }^{ \cos ^{ 2 }{ x }  }\sin { 2x }  } dx\quad $$


SOLUTION
Let 
$$t={\cos}^{2}{x}\Rightarrow\,dt=-2\cos{x}\sin{x}dx=-\sin{2x}dx$$

$$\displaystyle\int{{e}^{{\cos}^{2}{x}}\sin{2x}\,dx}$$

$$=-\displaystyle\int{{e}^{t}\,dt}$$

$$=-{e}^{t}+c$$ 

$$=-{e}^{{\cos}^{2}{x}}+c$$ where $$t={\cos}^{2}{x}$$
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Subjective Medium Published on 17th 09, 2020
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