Find the second degree polynomial P(x) that has the following properties: (a) P(0)=1, (b) P'(0)=0, (c) the indefinite integral ∫P(x)dx/(x^3(x-1)^2). Note: the the indefinite integral is a rational function. Cannot have Log terms occuring in solution. first. I use the generic polynomial aX^2+bx+c. When P(0)=1=C. Therefore C=1. Taking the derivative of the generic polynomial, P'(X)=2aX+B. When P'(0)=0=B. Therefore B=0. So far for the generic polynomial I have. P(X)= aX^2+1. for the integral:∫(aX^2+1)dx/(X^3(x-2)^2) breaking up the integral. ∫(aX^2)dx/(x^3(x-1)^2)+∫dx/(x^3(x-1)^2 =a∫dx/x(x-1)^2+∫dx/(x^3(x-1)^2). The problem is. No matter how I did the the integration by parts, either choice for u. I get a ln terms for solution. Is there something I missing?