Question

Evaluate the integral ; integral of (x^2+x+3)dx/ (x-1)^3

Answer 1

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

Answer 2

A/x-1 + B/(x-1)^2 + C/(x-1)^3... then

Answer 3

http://www.youtube.com/watch?v=qm3Gg42CKXI&feature=related

Answer 4

You're doing good, you want to know how to finish?

Answer 5

(x2+x+3)dx/(x−1)3 = A/x-1 + B/(x-1)^2 + C/(x-1)^3

Answer 6

Multiply through by \[(x-1)^{3}\]

Answer 7

don't I have to get rid of the fractions first ?

Answer 8

Multiplying by \[(x-3)^{3}\] is a way of getting rid of the fractions.

Answer 9

jk, thats what it does haha YEAH

Answer 10

now find out the variables right?

Answer 11

if x = 1, c = 5 but how do I find out the other variables

Answer 12

You substitute for 5 for C into the line \[x ^{2}+x+3=A(x-1)^{2}+B(x-1)+C\]

Answer 13

and expand

Answer 14

how do you expand ?

Answer 15

Multiply threw with B, expand \[(x-1)^{2}\]