Good News, I retried the example problem today and after a while I was able to get the answer. As you all suggested, I found that allowing

to be the simplest approach. I also now understand why the the numerator changed to

. It was so, to keep the fuction the same, but in terms of u.

I am now attempting, with slight difficulty, to try the other substition example by letting

=

Now I change the Numerator in terms of u.

Now I need to change the variables for the dx in terms of du but I am having troubles.

my first inclination was that since

, then du =

, then replace that x within the du to

=

=

So in the original function,

, the dx= 1, so I should set the dx = du???

1 =

, multiply both sides to isolute du in terms of u, so finally, du=

So Now I have

which is what the book also has

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In regards to finding the du, can I simply say Hey, the derivative of the numerator

is 2u and i tack it on to the back of the new integrand to get

???????

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Are these the correct logical steps I should take ?????