Just, the Integral of (x^3)/(x^3+1) dx
I know you can turn the denominator into (X+1)(X^2-x+1). What do you do from there? thanks =)
I doublechecked this but I'm a bit rusty lately so perhaps someone else can verify it,
int dx/(x+1)(x^2-x+1)
You have an irreducible quadratic factor so the equation is
a/(x+1) + (bx+c)/(x^2-x+1) = 1
x=0 -> a+c=1
x=1 -> a+2b+2c=1
x=-1 -> 3a=1
Solving that system, a=1/3, b=-1/3, c=2/3
Now all you have to do is to solve the last part:
int 1/(3(x+1)) + ((-1/3)x + (2/3))/(x^2-x+1)
Hope this helps