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to find integration of (1+(1/x*x))/(x*x+(1/(x*x))+3)

to find integration of
(1+(1/x*x))/(x*x+(1/(x*x))+3)

Question Image
Grade:12

2 Answers

Arun
25763 Points
one year 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
Vikas TU
14149 Points
one year ago
Dear student 
Hope your doubt gets cleared 
Please refer the solved examples of the below link 

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