Strategy to integrate something like (x^2+1)/sqrt(x-1)

[bouhrassa]

What strategy would you use to integrate something like : (x^2+1)/sqrt(x-1)

Is it possible to substitute u=sqrt(x-1) du = 1/2u ?
Or is there an other way ?

 

[Deleted member 4993]

What strategy would you use to integrate something like : (x^2+1)/sqrt(x-1)

Is it possible to substitute u=sqrt(x-1) du = 1/(2u) ?
Or is there an other way ?

u=√(x-1)is a good strategy - in my view.

 

[Steven G]

What strategy would you use to integrate something like : (x^2+1)/sqrt(x-1)

Is it possible to substitute u=sqrt(x-1) du = 1/2u ?
Or is there an other way ?

I assume you meant to write u=sqrt(x-1) , du = 1/2u . No, if u=sqrt(x-1) then du does not equal 1/2u. Sorry! du = (1/(2u))dx or dx = 2udu.

You can't integrate (x^2+1)/sqrt(x-1)!!! You can however integrate [(x^2+1)/sqrt(x-1)]dx. How can you substitute if you do not have each piece that needs to written in terms of u? Int[(x^2+1)/sqrt(x-1)]dx = int[((u+1)^2 + 1)/u]2udu