## cherrilyn 5 years ago Evaluate the integral ; integral of (x^2+x+3)dx/ (x-1)^3

1. cherrilyn

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

2. cherrilyn

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

3. anonymous
4. anonymous

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

5. anonymous

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

6. anonymous

Multiply through by $(x-1)^{3}$

7. cherrilyn

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

8. anonymous

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

9. cherrilyn

jk, thats what it does haha YEAH

10. cherrilyn

now find out the variables right?

11. cherrilyn

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

12. anonymous

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

13. anonymous

and expand

14. cherrilyn

how do you expand ?

15. anonymous

Multiply threw with B, expand $(x-1)^{2}$