Mathematics

Evaluate the following integral:
$$\displaystyle \int { \cfrac { \sin ^{ 2 }{ x }  }{ 1+\cos { x }  }  } dx$$


SOLUTION
$$\displaystyle\int{\dfrac{{\sin}^{2}{x}}{1+\cos{x}}dx}$$

$$=\displaystyle\int{\dfrac{1-{\cos}^{2}{x}}{1+\cos{x}}dx}$$

$$=\displaystyle\int{\dfrac{\left(1+\cos{x}\right)\left(1-\cos{x}\right)}{1+\cos{x}}dx}$$

$$=\displaystyle\int{\left(1-\cos{x}\right)dx}$$

$$=\displaystyle\int{\left(1\right)dx}-\int{\left(\cos{x}\right)dx}$$

$$=x-\sin{x}+c$$
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Subjective Medium Published on 17th 09, 2020
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