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## Homework Statement

Find the second degree polynomial P(x)

such that P(0)=1,P'(0)=0,and

[itex]\int[/itex]P(x)/{x

^{3}(x-1)

^{2}} dx

is a rational function

## Homework Equations

this chapter is about integration techniques,L'Hopital's Rule, and Improper Integral

partial fraction,partial integration are learnt.

## The Attempt at a Solution

Since P(x) is second degree polynomial,i let P(x)=Ax

^{2}+Bx+C

P(0)=1,so 1=A(0)+B(0)+c

C=1

P'(0)=0,so 2Ax+B=0,

B=0

So I know P(x) is Ax

^{2}+1,but i dont know how to do next on.Partial fraction is seem too many variables and have only 1 clue{P(0)=1},partial integration is hard too.I think "Rational function" is the key of this question,but i know rational fraction no more than it can be express as a/b,how to solve this question ?