Question

Integral of (3x^2+2x^3+3x-2)/{(x^2+2x+2)^2}?

Answer 1

I tried partial fraction decomposition but I couldn't get a single answer for the constants ( I got d = 0 and d = -1, for example )

Answer 2

\[\int\limits\frac{ x ^{3}+2x^{2} + 3x - 2 }{ (x ^{2}+2x+2)^{2} }\]

Answer 3

\[\frac{-x-2}{2 \left(x^2+2 x+2\right)}+\log \left(x^2+2 x+2\right)-\frac{7}{2} \tan ^{-1}(x+1) \]