Using python and only the Sympy library $($from sympy import $*),$ solve the following question:

a$)$ Find the partial fraction decomposition of the function $g(x)=\frac{x^2+2x+a}{(x-1{)}^3(x^2+1{)}^2},$ where $a$ is a positive real

constant.

b$)$ For what value of $a,$ does ${\displaystyle \underset{2}{\overset{4}{}}}g(x)dx=1?$