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forestmine
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Homework Statement
Evaluate the integral. (Remember to use ln |u| where appropriate.)
∫ds/s^2(s − 1)^2
Homework Equations
The Attempt at a Solution
I attempted a solution using the method of partial fractions, but it seems my answer is wrong. Here's what I did...
1=A/s +B/s^2+C/(s-1)+D/(s-1)^2
Then multiplying by a common denominator,
1=As(s-1)^2 +B(s-1)^2 +Cs^2(s-1) + Ds^2
1=A(s^3-2s^2+s) + B(s^2 - 2s +1) + C(s^3 -s^2) +Ds^2
Equating the coefficients and solving for A, B, C, and D, I get A=1, B=1, C=-1, D=3
So my integral now looks like
∫1/s+1/s^2-1/(s-1)+3/(s-1)^2
And taking the integral, I got
lns - 1/s - ln(s-1) + 3/(s-1)
which evidently is wrong.
If anyone can point me in the right direction in terms of where I went wrong, it would be greatly appreciated.
Thanks!