# Thread: inverse trig integration:two methods=two diff ans HELP!!

1. Originally Posted by i_zz_y_ill
when u take 4 out side with the 3/4,,,,,,,,(this is jhevs method), doesnt it become
3/4 (integral) 1/((3x+1)^2)/4 + 1

not 3/3 (integral) 1/((3x+1)^2)/2 +1
It should read 1/ [(3x+1)/2]^2 + 1

2. Originally Posted by i_zz_y_ill
when u take 4 out side with the 3/4,,,,,,,,(this is jhevs method), doesnt it become
3/4 (integral) 1/((3x+1)^2)/4 + 1

not 3/3 (integral) 1/((3x+1)^2)/2 +1
ok, look carefully at what i did. i never typed $\displaystyle \frac {(3x + 1)^2}2$, i typed $\displaystyle \left( \frac {3x + 1}2 \right)^2$. BIG difference

$\displaystyle \frac {(3x + 1)^2}4 = \frac {(3x + 1)^2}{2^2} = \left( \frac {3x + 1}2 \right)^2$

3. ## uhuh

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?

4. See my signature for LaTeX typesetting, really, see it to make your posts clearer.

5. Originally Posted by i_zz_y_ill
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 if so then BOLLOCKS to that.. what i actually mean is BOLLOCKS TO THAT!!!!!
????
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.

6. ## I Totally Gottit Triumph

U HAVE TO SUBSTITUTE U=3X+1
DX=DU/3 CANCELS + GIVES ANSWER PRESUMABLY I MUST SUBSTITUTE WHENEVER THERE A COEFFICIENT OF X IN THOSE BRACKETS!?

7. Effectively, you could put it that way, yes, or you could just do it in your head =)

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