Question

evaluate the integral

Answer 1

\[\int\limits_{?}^{?}100xdx/(x-3)(x ^{2}+1)^{2}\]

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

Answer 2

are you sure?

Answer 3

oops I mean A/x-3 + Bx+C/x^2+1 + Dx+E/(x^2+1)^2

Answer 4

lol

Answer 5

alright, good , now start taking small values for x ^_^ to find A, B, C and D

Answer 6

wait, first you have to multiply the denominator on all parts

Answer 7

Take x=3. You will find A directly.

Answer 8

A=3

Answer 9

so, you'll get :\[100x = A(x+1)^2 + Bx + C(x-3)(x^2+1) + Dx + E (x-3)\]

Answer 10

ok A=3 :)

Answer 11

wait no

Answer 12

now you can take values for x to find all the alphabets ^_^

Answer 13

hmm, what?

Answer 14

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

Answer 15

and Distribute (x-3) to the Dx AND the E?

Answer 16

hmm, I think it's the whole thing

Answer 17

yes yes, I'm sure

Answer 18

okay so A is indeed 3

Answer 19

yes it is ^_^

Answer 20

The better way is to open all brackets, and add like terms together.

Answer 21

now take other values for x, such as -1 1 2 -2 ~

Answer 22

B=0

Answer 23

Oh wait!!

Answer 24

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

Answer 25

yes it's a must, you need to get all the values, A, B,C,D,and E

Answer 26

I mean the numbers -1, 1, 2, and -2

Answer 27

yes , you must lol, what other way is there to solve it?

Answer 28

you must check with all values my dear :)

Answer 29

B=-3

Answer 30

C=9

Answer 31

you checked the values? anwar? or shall I check after you lol

Answer 32

D=18

Answer 33

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

Answer 34

no you're write, so now you have equation 1, you can use it later to either subtract or add from another equation ^_^

Answer 35

right*

Answer 36

alright I gtg, I'll be back later, bye ^_^

Answer 37

okay thankss! Ttyl :)

Answer 38

anwar will continue, most welcome :)

Answer 39

I got all of them. Hopefully right!

Answer 40

A=3, B=-3, C=9, D=24, E=-8

Answer 41

Bye starica!!

Answer 42

thanks anwar!

Answer 43

You're welcome!! You may want to check them.

Answer 44

OMG, Sorry there was a mistake.

Answer 45

It should be:
A=3, B=-3, C=-9, D=-30, E=10.
Sorry for the confusion.

Answer 46

what values for x did you use?

Answer 47

Well.. I opened all the parenthesis, and add like terms together, and then solved the equations.

Answer 48

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.