Mathematics

Evaluate:
$$\int { \left[ \sin { \left( \log { x }  \right)  } +\cos { \left( \log { x }  \right)  }  \right]  } dx$$


SOLUTION
$$I=\displaystyle \int \sin(\log x)+\cos(\log x)dx$$ 
   $$\log x=t$$ 
       $$x=e^{t}$$ 
   $$dx=e^{t}dt$$ 
   $$\therefore I=\displaystyle \int (\sin t+\cos t)e^{t}dt$$
      $$=\displaystyle \int d(\sin te^{t})$$ 
      $$=\sin te^{t}+c$$ 
      $$=x \sin(\log x)+c$$
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Subjective Medium Published on 17th 09, 2020
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