k look at this example, i shud be able to do this without substitution....
using (INT) 1/(a^2 + (f(x))^2 ) = 1/a arctan x/a
i can say that (int) 4/(x^2 -2x + 3)dx = 4(int) 1/(x-1)^2 +2 dx
there = 4/root2 arctan (x-1)/root2 + c
which is correct,, are you saying thatbecause with my previous example the
f(x) has a coefficient if you like of three before it i have to use substitution?
Nope, you don't have to use substitution if you can remember to deal with the coefficient later on (i.e. divide by 3). Jhevon did a great job illustrating the basic principles behind his solution, and it's very comprehensive - but ultimately you don't have to use substitution if you know how to solve it otherwise.