How do you factor out dx in the arc length integral?

[derek181]

I am just learning how to find lengths of curves using calculus. √((dx)²+(dy)²)→∫√(1+(dy)²)dx. My question is how are you able to bring out the dx. Is this some sort of algebraic trick I've never heard of. Can someone please explain this to me?

 

[derek181]

nevermind, you just multiply by dx/dx

 

[mathman]

You should have √(1+(dy/dx)²) for the second integrand.

 

[Boson]

It is [{1+(dy/dx)^2}^0.5]dx = Length of curve