Real partial fraction decomposition/Primitive function/x to x^5+3x^3-2x^2+x-1 over (x-1)^2(x^2+1)/Exercise

We consider the function

$f\colon \mathbb {R} \setminus \{1\}\longrightarrow \mathbb {R} ,x\longmapsto {\frac {x^{5}+3x^{3}-2x^{2}+x-1}{(x-1)^{2}(x^{2}+1)}}.$

a) Determine the real partial fraction decomposition of ${}f$.

b) Determine an antiderivative of ${}f$ for ${}x>1$.

Create a solution