Extracting a constant variable from integral

[shanepitts]

Sorry for the simplicity of the question but I encountered a simple math problem whilst autodidacting myself on classical physics. I seen that a surplus of a specific constant variable "b" was extracted from an integral after a bit of manipulation.

∫xdx was turned into b²∫(x/b)d(x/b)

Does the extra constant b come from the d(x/b)? If so, or if not, how can one change what the integral is being integrated with respect to?

This question is a not a homerwork question.

Thank You

 

[Paul Eccles]

If b is a constant, then yes that is valid. We can change the variable you are integrating with respect to, with substitution, and it's a nifty trick for integrals.

d(x/b) is jus dx/b or (1/b) dx so you can take the constant term out like that.

 

[shanepitts]

If b is a constant, then yes that is valid. We can change the variable you are integrating with respect to, with substitution, and it's a nifty trick for integrals.

d(x/b) is jus dx/b or (1/b) dx so you can take the constant term out like that.

Awesome, thanks a bunch