I am currently working on an integral that I finally found the answer to after approaching differently, but I would like to know why my first approach failed -- it led to undefined trig functions and/or ln 0. As far as I can tell, by math logic is okay, unless I'm missing something.

My initial approach was to multiply by leading to and then to and then to . Rewriting, . This leads to . But when I attempted to integrate, it failed. Simple u-subst. works u = 1 + sint,

du = cost dt, but why does the other approach fail?