Mathematics

Write a value of 
$$\int { { e }^{ \log { \sin { x }  }  }\cos { x }  } dx$$


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

$$I=\displaystyle\int{{e}^{\log{\sin{x}}}\cos{x}dx}$$

$$=\displaystyle\int{{e}^{\log{t}}dt}$$

$$=\displaystyle\int{t\,dt}$$

$$=\dfrac{{t}^{2}}{2}+c$$    .......where $$c$$ is the constant of integration.

$$=\dfrac{{\sin}^{2}{x}}{2}+c$$    .......where $$t=\sin{x}$$
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Subjective Medium Published on 17th 09, 2020
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