Cases in which constants can absorb terms

[Duderonimous]

Homework Statement

What are the cases in which constants of integration can and cannot absorb terms and operations and just be redefined as c.

Homework Equations

The Attempt at a Solution

As long as I keep redefining my constant of integration I can say

-c=k

ac=k where in any constant including zero

c^(a)=k

Can I say
1/c=k?
ln|c|=k?
sin(c)=k (or any trig function for that matter)

or for these last examples do I need to define the domain of c

 

[tiny-tim]

Hi Duderonimous!

… or for these last examples do I need to define the domain of c

Yes.

But it's usually fairly obvious what you can do.

eg, if it's + 1/C, then obviously C = 0 is a problem that you'll have to deal with separately

(and you'll probably have to deal with C > 0 and C < 0 separately also)