Mathematics

# Evaluate the following integral$\int { \cfrac { \sec ^{ 2 }{ x } }{ \tan { x } +2 } } dx$

##### SOLUTION
Let
$t=\tan{x}+2\Rightarrow\,dt={\sec}^{2}{x}dx$

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

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

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

$=\log{\left|\tan{x}+2\right|}+c$ where $t=\tan{x}+2$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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