- #1
demersal
- 41
- 0
Homework Statement
[tex]\int[/tex]1/(s[tex]^{2}[/tex](s-1)[tex]^{2}[/tex]) ds
Homework Equations
Partial Fractions
The Attempt at a Solution
= [tex]\frac{A}{s^{2}}[/tex]+[tex]\frac{B}{s-1}[/tex]+[tex]\frac{C}{(s-1)^{2}}[/tex]
Setting numerators equal to each other:
1 = A(s-1)(s-1)[tex]^{2}[/tex] + Bs[tex]^{2}[/tex](s-1)[tex]^{2}[/tex]+Cs[tex]^{2}[/tex](s-1)
1=(As-A)(s[tex]^{2}[/tex]-2s+1)+Bs[tex]^{2}[/tex](s[tex]^{2}[/tex]-2s+1)+Cs[tex]^{3}[/tex]+Cs[tex]^{2}[/tex]
1=As[tex]^{3}[/tex]-2As[tex]^{2}[/tex]+As-As[tex]^{2}[/tex]+2As-A+Bs[tex]^{4}[/tex]-2Bs[tex]^{3}[/tex]+Bs[tex]^{2}[/tex]+Cs[tex]^{3}[/tex]-Cs[tex]^{3}[/tex]+Cs[tex]^{2}[/tex]
1=Bs[tex]^{4}[/tex]+(A-2B+C)s[tex]^{3}[/tex]+(-3A+B-C)s[tex]^{2}[/tex]+3As-A
Using coefficients to solve for variables (here's where something is up!)
s[tex]^{4}[/tex]: 0=B
s[tex]^{3}[/tex]: 0=A-2B+C
s[tex]^{2}[/tex]: 0=-3A+B-C
s: 0=3A
#: 1=-A
They don't add up! Am I doing something wrong?
Thank you for everyone's time and help!