resolve the partail fraction and then integrate.3x^2-34x+97/(x-5)^3
The fraction is:
p(x)/(x-5)^3
with
p(x) = 3x^2-34x+97
Then let's expand p(x) in powers of (x-5). If we put x = 5+t then we have:
p(5+t) = 2 - 4 t + 3 t^2
Therefore, partial fraction expansion is:
2/(x-5)^3 - 4/(x-5)^2 + 3/(x-5)