Consider the region R bounded by y = 1 / (x^2 + 3x + 2) , x = 0, x = 1 and the x-axis.

Express your answer exactly with at most one logarithm in the answer.

Find the volume of the solid formed by rotating R about the x-axis.

I need help with this problem.

I believe I am supposed to take the integral from 0 to 1 of pi(1 / (x^2 + 3x + 2))dx

I use partial fraction decomposition and get ...

1 = A(x+3)(x-1)^2 + B(x-1)^2 + C(x+3)^2(x-1) + D(x+3)^2

From substituting x = 1, D = 1/16

and x = -3, B = 1/16

I need help finding A and C. and I am also wondering if my reasoning is correct so far.