Question

How do you use substitution to integrate `1/sqrt(x^2 -4)`?

Answer 1

ln I`x/2 +sqrt(x^2-4)/2`I +C

Explanation:

Let x= 2sec u. so that dx= 2sec u tan u du. The given integral becomes `int 1/sqrt (4sec^2 u -4) 2 sec u tan u du`

= `int secu du`

= ln lsecu +tan u I +C

= ln I`x/2 + sqrt(x^2-4)/2`I +C