you make a mistake, you only can use partial fractions when in the denominator is in factors, and in your problem has sums
integral (x^2+1)/[(x^2+x+1)^2 + (x-2)^2]
what i tried is :
A/(x-2) + B/(x-2)^2 + (Cx+D)/(x^2+x+1) + (Ex+F)/(x^2+x+1)^2
then try to find ABCDEF
its seems too long and complicated is there any better way to solve it pls
There are no simple ways to obtain the remaining terms in this problem.
All techniques are more or less the same.
You can just multiply out and set the two polynominals equal to each other.
Then if you wish you can use matrices to solve for A...F.
Or one idea I never see people do, but it works.
Just let x=0,1,2,3,4, what ever it takes.
This too creates 6 equations and 6 unknows.
BUT you have no choice in this.
You can only steal the F.
i expanded the whole equation and then organized it to this form
A(x^5-3x^4+x^3+4x) + B(x^4-3x^3+x^2+4) + C(x^3-4x^2+4x) +D(x^2-4x+4) +E(x^5-x^3-4x^2+5x-2) +F(x^4+2x^3+3x^2+2x+1) = x^2 + 1
from this i got the following
A+E =0 (for x^5)
-3A+B+F =0 (for x^4)
A-3B+C-E+2F =0 (for x^3)
B-4C+D-4E+3F =1 (for x^2)
4A+4C-4D+5E+2F=0 (for x)
4B+4D-2E+F =1 (for cnst)
ok i already got E as u explained (E=5/7)
and started to substitute
in the equations above so i got
is that right or just a mess