Solving 4X^3-7X^2+6X-3 by Hand

[thharrimw]

How colud you intergrate (4X^3-7X^2+6X-3)/(X^6-4X^3) by hand (my TI-89 gave me -[2(13*2^(1/3)-12)(√3*2^(1/3))X^2*Arctan[√3-*2^(1/3)(2X+2^(2/3))/6]+2^(2/3)+28√2+13)X^2ln(X62+2^2/3X+X^(4/3)+2(2^(1/3)(14*2^(2/3)*X^2ln|X-2^(2/3)|-6(14X^2ln|X|)+2(4X-1)))))]\96X^2
i tryed to use partial fractions but i couldn't solve it using partial fractions so i have no idea of where to start.

 

[lurflurf]

partial fractions works fine, what went wrong?

 

[thharrimw]

never mind I messed up on my simplification i put a extra variable when i simplified so i got
0=A+E,
4=B+D,
-7=C-4E,
6=4D+E,
-3=-4c+A,
insted of
0=A+E,
4=B+D,
-7=C-4E,
6=4D,
-3=-4c,