Mathematics

# Integrate : $\displaystyle \int { \frac { 1+\tan { x } }{ x+\log { \sec { x } } } dx }$

##### SOLUTION
Given : $\displaystyle \int { \frac { 1+\tan { x } }{ x+\log { \sec { x } } } dx }$

Let  $I=\displaystyle \int { \frac { 1+\tan { x } }{ x+\log { \sec { x } } } dx }$

Let $t=x+\log{\sec{x}}$

$\Rightarrow dt=\left(1+\dfrac{1}{\sec{x}}\sec{x}\tan{x}\right)dx$

$\Rightarrow dt=\left(1+\tan{x}\right)dx$

$\displaystyle \int{\dfrac{\left(1+\tan{x}\right)dx}{x+\log{\sec{x}}}}$$=\displaystyle \int{\dfrac{dt}{t}}$

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

where $(t=x+\log{\sec{x}})$

$I=\log{\left|x+\log{\sec{x}}\right|}+c$

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

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