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
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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