evaluate the integral

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evaluate the integral

Mathematics
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\[\int\limits_{?}^{?}100xdx/(x-3)(x ^{2}+1)^{2}\] I know I change it to A/x-1 + B(x-1)^2+C(x-1)^3 then multiply it by (x-1)^3 then what
are you sure?
oops I mean A/x-3 + Bx+C/x^2+1 + Dx+E/(x^2+1)^2

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Other answers:

lol
alright, good , now start taking small values for x ^_^ to find A, B, C and D
wait, first you have to multiply the denominator on all parts
Take x=3. You will find A directly.
A=3
so, you'll get :\[100x = A(x+1)^2 + Bx + C(x-3)(x^2+1) + Dx + E (x-3)\]
ok A=3 :)
wait no
now you can take values for x to find all the alphabets ^_^
hmm, what?
when you distribute in..for example.. Bx+C(x-3)(x^2+1) ... do you distribute the two things in the parenthesis to the Bx AND the C? or just the C
and Distribute (x-3) to the Dx AND the E?
hmm, I think it's the whole thing
yes yes, I'm sure
okay so A is indeed 3
yes it is ^_^
The better way is to open all brackets, and add like terms together.
now take other values for x, such as -1 1 2 -2 ~
B=0
Oh wait!!
blaah do I have to test all of those numbers? lol its kiind of hard to predict the right values just by looking at it
yes it's a must, you need to get all the values, A, B,C,D,and E
I mean the numbers -1, 1, 2, and -2
yes , you must lol, what other way is there to solve it?
you must check with all values my dear :)
B=-3
C=9
you checked the values? anwar? or shall I check after you lol
D=18
Okay If I plug in A=3 and x=-1..... I get -100=12+2B-2C+4D-4E. now what? Or am I doing this wrong
no you're write, so now you have equation 1, you can use it later to either subtract or add from another equation ^_^
right*
alright I gtg, I'll be back later, bye ^_^
okay thankss! Ttyl :)
anwar will continue, most welcome :)
I got all of them. Hopefully right!
A=3, B=-3, C=9, D=24, E=-8
Bye starica!!
thanks anwar!
You're welcome!! You may want to check them.
OMG, Sorry there was a mistake.
It should be: A=3, B=-3, C=-9, D=-30, E=10. Sorry for the confusion.
what values for x did you use?
Well.. I opened all the parenthesis, and add like terms together, and then solved the equations.
For example if you have x^2(A+B)+x(C+2B)=5x^2+x, that means: A+BC=5 and C+2B=1.. I used this idea.

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