Mathematics

Evaluate the following integral:
$$\int { \cfrac { \sin { \left( \log { x }  \right)  }  }{ x }  } dx\quad $$


SOLUTION
Let 
$$t=\log{x}\Rightarrow\,dt=\dfrac{dx}{x}$$

$$\displaystyle\int{\dfrac{\sin{\left(\log{x}\right)}}{x}dx}$$

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

$$=-\cos{t}+c$$

$$=-\cos{\left(\log{x}\right)}+c$$ where $$t=\log{x}$$
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Subjective Medium Published on 17th 09, 2020
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