In both the approachs you get the same answer.
Intg(secθ) - Intg(tanθ)
= ln(secθ + tanθ) -ln(secθ)
= ln[(secθ + tanθ/secθ]
= ln[ 1 + sinθ]
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?