Mathematics

# Evaluate the following integral$\int { \cfrac { cosec ^{ 2 }{ x } }{ 1+\cot { x } } } dx\quad \quad$

##### SOLUTION
Let
$t=1+\cot{x}\Rightarrow\,dt=-{\csc}^{2}{x}dx$

$\displaystyle\int{\dfrac{{cosec}^{2}{x}\,dx}{1+\cot{x}}}$

$=-\displaystyle\int{\dfrac{dt}{t}}$

$=-\log{\left|t\right|}+c$

$=-\log{\left|1+\cot{x}\right|}+c$ where $t=1+\cot{x}$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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