- #1

Youngster

- 38

- 0

## Homework Statement

[itex]\int[/itex][itex]\frac{8x^{2}+5x+8}{x^{3}-1}[/itex]

## Homework Equations

Because the denominator can be reduced to (x-1)([itex]x^{2}+x+1[/itex]), I set up the partial fractions to be [itex]\frac{A}{(x-1)}[/itex] + [itex]\frac{Bx+C}{(x^{2}+x+1)}[/itex]

## The Attempt at a Solution

I've solved for A, B, and C, and now have the integral set up as such:

7[itex]\int\frac{dx}{x-1}[/itex] + [itex]\int\frac{x-1}{x^{2}+x+1}[/itex]dx

Where A is 7, B is 1, and C is -1

I can integrate the first term simply, but I'm having trouble figuring out how to integrate the second term. The best I can think of is a u substitution, but du turns into 2x+1 dx, which is nothing like x-1 dx. Any suggestions?