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

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• Apr 1st 2008, 05:34 PM
h2osprey
Quote:

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
• Apr 1st 2008, 05:36 PM
Jhevon
Quote:

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

$\displaystyle \frac {(3x + 1)^2}4 = \frac {(3x + 1)^2}{2^2} = \left( \frac {3x + 1}2 \right)^2$
• Apr 1st 2008, 05:55 PM
i_zz_y_ill
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?
• Apr 1st 2008, 05:57 PM
Krizalid
See my signature for LaTeX typesetting, really, see it to make your posts clearer.
• Apr 1st 2008, 06:08 PM
h2osprey
Quote:

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.
• Apr 1st 2008, 06:11 PM
i_zz_y_ill
I Totally Gottit Triumph
(Bow)(Bow)(Bow)(Handshake) 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!?
• Apr 1st 2008, 06:24 PM
h2osprey
Effectively, you could put it that way, yes, or you could just do it in your head =)
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