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Sir How to solve this And how to approach these type of question

Sir How to solve this 
And how to approach these type of question 

Question Image
Grade:12

1 Answers

Aditya Gupta
2080 Points
2 years ago
so simply put 1+1/x=y^2
so we have 2y*dy/dx= -1/x^2= – (y^2 – 1)^2
so integral becomes
 –y*2ydy/(y^2 – 1)^2
now write the denominator as (y – 1)^2*(y+1)^2
now use partial fractions and write the entire function of y as 
A/(y – 1)+B/(y – 1)^2+C/(y+1)+D/(y+1)^2
after that the integral is trivial and simply replace y as root(1+1/x) to obtain the final answer.
 

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