I solved the problem the 3's are part of the constant c thats why they arent in the answer.

Hello,

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.