Mathematics

Evaluate the following integrals:
$$\int { \cfrac { \cos { 2x }  }{ \sqrt { \sin ^{ 2 }{ 2x } +8 }  }  } dx$$


SOLUTION
Now,

$$\int { \cfrac { \cos { 2x }  }{ \sqrt { \sin ^{ 2 }{ 2x } +8 }  }  } dx$$

$$=\dfrac{1}{2}\int { \cfrac { 2\cos { 2x }  }{ \sqrt { \sin ^{ 2 }{ 2x } +8 }  }  } dx$$

$$=\dfrac{1}{2}\int { \cfrac { d(\sin { 2x } ) }{ \sqrt { \sin ^{ 2 }{ 2x } +8 }  }  } $$

$$=\dfrac{1}{2}\log|(\sin 2x)+\sqrt{\sin^2 2x+8}|+c$$. [ Where $$c$$ is integrating constant]
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Subjective Medium Published on 17th 09, 2020
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