I am having issues with some problems with the integration of natural logs/substitution. I was fine at the beginning of the chapter, but now I'm having some problems. These are a few examples of the type I'm stuck on:

1) The integral of (1/(1+2x^(1/2))dx

2) The integral of (cot(theta/3))d-theta

For the first I tried substitution and got u=1+2x^(1/2), but the du is what is confusing me. I'm just not sure how to proceed.

And the second one I realize you change cot into cos/sin, but I'm confused as to why in the answer a 1/3 (and a 3 to counteract it) is added to the integral? I'm just confused with the process...

If anyone could kindly guide me in the right direction, I would be forever thankful!

Last quiz of the semester is tomorrow morning and I really want to do well on it!