- #1

flyingpig

- 2,579

- 1

## Homework Statement

I thought I understood what it means to multipyl and divide something, but lately I think it's wrong.

Mostly in Calculus, there are functions that can't be integrated unless we multiply and divide by something. Usually trig integrals need that, but even a simple integral like

[tex]\int_{0}^{1} dx[/tex]

Can go wrong if we multiply and divide by the same thing. Also most of the time we aren't just multiplying and dividing by a number, we do a variable.

For instance, to the above integral, if I go ahead and multiply and divide x (x/x) then that integral becomes undoable.

Often we take granted to use this trick, but sometimes it doesn't work.

How does one recognize it if the function we are "integrating" creates a problem(especially if it is very very complicated)? How do we catch the mistake?