Mathematics

Write a value of 
$$\displaystyle\int { \cfrac { \sin { x }  }{ \cos ^{ 3 }{ x }  }  } dx$$


SOLUTION
$$I=\displaystyle\int{\dfrac{\sin{x}}{{\cos}^{3}{x}}dx}$$

$$=\displaystyle\int{\tan{x}{\sec}^{2}{x}dx}$$

Let $$t=\sec{x}\Rightarrow\,dt=\sec{x}\tan{x}dx$$

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

$$=\dfrac{{t}^{2}}{2}+c$$

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