indefinite integral of the sqrt((x+3)/(x+1))dx

Question

it is a mathematical question needs an expert to be solved 

 

Answer 1

This is a nasty one...however if you substitute u = x + 3 ; du = dx

 

you get sqrt(u/(u-2))

 

This has a solution I found in an integral table...but I can't derive it for you

 

after plugging in and putting back in x + 3 for u I get,

 

sqrt((x+3)/(x+1)) + 2ln(sqrt(x+3) + sqrt(x+1))

 

I come from the physics world where integral tables are our best friends =)