I solved the problem the 3's are part of the constant c thats why they arent in the answer.
I have the integral
dy / sqrt( 9 + y^2)
I have worked it all the way down to
ln| sec theta + tan theta| + C
I need to now put it in terms of y.
from my previous work during the problem I have
y= 3 tan theta
so using right triangle trig
tan theta= y/3
hypotenuse is sqrt(9+y^2)
the answer I get is ln|(sqrt(9+y^2)/3) + (y/3)| + C
the book answer is ln|sqrt(9 + y^2) + y| + C
could someone please explain. I think I am having a misunderstanding with my substitutions.