Question

use long division to write f(x) as the sum of a polynomial and a proper rational function. Then calculate the integral of f(x)d(x). EQUATION: f(x) = x^3-1 / x^2-x. I did long division and got -x-1 = A(x-1) + B(x) and so x = 1 and x = 0. What should I do next?

Answer 1

when I do the division i end up with:

x + 1 + (1/x)

Answer 2

then you intergrate the seperate terms:

x^2/2 +x +ln(x) +C

Answer 3

x^2 -x goes into x^3 - 1 x times with a remainder of -x-1 right?

Answer 4

x +1 + (x-1)/x(x-1)
--------------
x^2 -x | x^3 -1
-x^3 +x^2
-----------
x^2 -1
-x^2+x
---------
x-1

Answer 5

remember to "subtract" the result :)

Answer 6

[S] x + 1 + (1/x) dx

(x^2)/2 +x +ln(x) +C

Answer 7

ooooooh Wow okay! Thanks!