Question

Why does U-substitution for integration work?

Answer 1

Why not?

Answer 2

are you looking for an explanation in simple terms, or a formal answer for a homework assignment?

Answer 3

An explanation in simple terms please.

Answer 4

Alright, just a moment.

Answer 5

If we take a problem such as \[\int\limits_{1}^{3} \frac{ 2x }{ x^{2}+1 }dx\] it would be time consuming to solve properly, yes?

Answer 6

yes, definitely.