Mathematics

# Evaluate the following integral$\int { \cfrac { \sec { x } \tan { x } }{ 3\sec { x } +5 } } dx$

##### SOLUTION
$I=\displaystyle\int{\dfrac{\sec{x}\tan{x}}{3\sec{x}+5}dx}$

Let $t=3\sec{x}+5\Rightarrow\,dt=3\sec{x}\tan{x}\,dx$

$\Rightarrow\,\dfrac{dt}{3}=\sec{x}\tan{x}\,dx$

$I=\dfrac{1}{3}\displaystyle\int{\dfrac{dt}{t}}$

$I=\dfrac{1}{3}\log{\left|t\right|}+c$

$I=\dfrac{1}{3}\log{\left|3\sec{x}+5\right|}+c$ where $t=3\sec{x}+5$

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