Evaluate the Integral $\int_{0}^{1} \frac{3 x^{3}+9 x^{2}+13 x+5}{(x+1)^{2}\left(x^{2}+1\right)} d x$

Evaluate the integral. $\int_{0}^{1} \frac{3 x^{3}+9 x^{2}+13 x+5}{(x+1)^{2}\left(x^{2}+1\right)} d x$