Could someone help me out by listing the order for U-Substitution Rules? I mean what over-rides what? I know that typically we

1) Let u= inside of parenthesis

2) Let u= exponents on e or a

3) Let u= angle on trig functions

4) Let u= denominator if no parenthesis

Here is where the confusion comes in. What if you have fraction with a trig or inverse trig function in it? Which one should be "U"? What if you have a trig function and a square root in an equation? There has to be some since of organization in this. I know that I have only been working with substitution for less than 24 hours, but I am obsessed at picking it up...

I spent 45 minutes on this one problem going back and fourth and finally I got the correct answer.

I initially thought of substituting 1+x^2 but there was no way I could get the problem worked out. If you do this and you end up getting (1/2)du=x*dx I don't think it is legal to insert the (1/2) inside of the trig function?

Thank You

-qbkr21