how to solve this into partial fractions I'm having a bit of a hard time putting this into partial fractions:
$$\frac{10}{x^2+2x+1+\pi^2}.$$
I know that the roots of the denominator are $-1 \pm i\pi$, but I dont know how to proceed on puting this in partial fractions. Can anyone here help me, please?

\begin{gather*}
I=\frac{10}{x^{2} +2x+1+\pi ^{2}} =\frac{10}{( x+1+i\pi )( x+1-i\pi )}\\
=\frac{10}{2i\pi }\frac{2i\pi }{( x+1+i\pi )( x+1-i\pi )}\\
=\frac{10}{2i\pi }\frac{( x+1+i\pi ) -( x+1-i\pi )}{( x+1+i\pi )( x+1-i\pi )}\\
=\frac{10}{2i\pi }\left(\frac{1}{( x+1-i\pi )} -\frac{1}{( x+1+i\pi )}\right)
\end{gather*}
