Question

find the volume of the resulting solid if the region under the curve y =1/(x^2 +3x +2) from x=0 to x=1 is rotated about the x axis

Answer 1

might have to decompose the fraction

Answer 2

Another ugly one. The guy/gal setting your assignment is a sadist.

Of course the volume is
\[\pi \int\limits_0^1 \frac{1}{(x^2 + 3x + 2)^2} \ dx\]

Answer 3

Now x^2 + 3x + 2 = (x+1)(x+2)

So look for the partial fraction decomposition and grind away.

If Wolfram hasn't made an error, this solution gives you something to aim towards for the indefinite integral:
http://www.wolframalpha.com/input/?i=integral+%281%2F%28x^2+%2B+3x+%2B+2%29^2%29