gah, integration (1 Viewer)

[Grey Council]

humph

trying to do integration

hanyway, got stuck on this

integrate:

4dx / ((x-1)^2(x+1)^2))

I can't seem to do it.

I know, its pretty easy, but i'm confused.

on a side note, what textbook is good to teach yourself integration from? Well, I have a basic knowledge of the theory of integration, but sometimes I get confused, like here, and I'm using the coroneos book. Thing is, Coroneos covers partial fractions in the first book, and then in this integration topic it just says go and revise. I'm having enough trouble with integration, thank you very much. I don't need another set of exercises to teach myself.

 

[McLake]

EDIT: The stress of my exam must of caused me to write crazy stuff. Ignore what was here before ...

 

[Grey Council]

um, yes?

anyway, I'm trying to teach myself integration by partial fractions. :-\

 

[McLake]

Originally posted by Grey Council
um, yes?

anyway, I'm trying to teach myself integration by partial fractions. :-\

This isn't partial fractions.

I have to go to uni now (exam, urg!) but i'll right an explination when I get home.

 

[Grey Council]

-.-

huh?

Its in my coroneos book

lol

I'll write it again:

numerator: 4.dx
denominator: (x-1)²(x+1)²

integrate that
:-\

BERLODOY HELL, thats it, I'm skipping partial fractions.
*moves onto trig integrals thingies*

 

[Grey Council]

whisht, tried that question again.
is it long or what?

 

[Constip8edSkunk]

part frac:
(Ax+B) / (x^2 - 1) + {Cx+D) / (x^2+1)
=(Ax+B)x^2+2(Ax+B)x+Ax+B+(Cx+D)x^2-2(Cx+D)x+Cx+D
=(A+C)x^3+(B+D+2(A-C))x^2 +(2(B-D)+(A+C))x+(B+D) = 4

clearly A+C = 0 and B+D = 4 by looking at leading coeficient and the const. term
then from the middle 2 coefficients we get A-C = -2 and B-D =0

2 sets of simultaneous eq. :
A=-1,B=1,C=D=2

so integrand bcomes (x+2)/(x+1)^2 - (x-2)/(x-1)^2
=1/2 * (2x+2)/(x+1)^2 - 1/2 * (2x-2)/(x-1)^2 + 1/(x+1)^2 + 1/(x-1)^2

integrate to get

ln|x+1| - ln|x-1| - 1/(x+1) - 1/(x-1) + c
= ln|(x+1)/(x-1)| - 1/(x+1) - 1/(x-1) + c

edit: revised

 

[Grey Council]

oh shit

i'm dead

I'm gonna need tuition

well, if your reading this, go check the buy/sell forum

 

[Grey Council]

slide rule is right

the point is, HOW to do?

 

[turtle_2468]

The long way: by partial fractions. Which isn't hugely long anyway... I'd suggest that. Unless you want to muck around with it, which is tricky...

 

[Grey Council]

fair enough.

I figured that I had gotten the hang of the concept, and skipped it.

hrm, do they ask you that sort of question in an exam?

 

[Constip8edSkunk]

ah yeah i reduntly repeated a line or 2 in the middle there... fixed...

ive never did a test with a straight partial fraction q outside q1 (in my memory anyway), and those are generally the standar ones