Du Smaller than Dx Integration Problem

Du Smaller than Dx Problem

Reasoning Behind the Problem (according to the book):

Answer

But have no clue what's going on (in any of it). Any hints? Of course I understand what to do if du = dx at the start. In that case, you do nothing. However, if du is bigger than dx than you multiply the dx by a constant, and then balance it with the reciprocal (of the constant) in the answer.

Re: Du Smaller than Dx Integration Problem

You started to make a u-substitution, but you should have instead of . If you solve for x in terms of u, you get x=u-1. So you have everything you need to make the substitution:

It's a little easier to see how to proceed now.

The book doesn't make the substitution. It just uses x+1 "as is" instead of u. But the steps are the same.

Hope this helps,

Hollywood