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to find integral of funtion (1+1/x*x)/(x*x+1/x*x +3)

to find integral of funtion
(1+1/x*x)/(x*x+1/x*x +3)

Grade:12

3 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
4 years ago
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Arun
25750 Points
4 years ago
 
Dear student
 
in denominator x^2 + 1/x^2 – 2 + 5
 
= ( x – 1/x)^2 +( sqrt5)^2
 
now coming to the Question
 
put x – 1/x = t
(1 + 1/x^2 ) dx = dt
 
dt/ t^2 + (sqrt5)^2
 
= 1/ sqrt(5) tan^-1 (t/sqrt5)
 
now put t = x – 1/x
 
Hope it helps
 
Thanks and regards
Vikas TU
14149 Points
3 years ago
Dear student 
Hope your doubt gets cleared 
Please refer the solved examples of the below link 

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