I have this integral:
\begin{equation*} \int \! \frac{x-1}{(x+1)(x^2+9)} \, \mathrm{d}x. \end{equation*}
I already split the denominator into two factors. Now, when I do partial fraction decomposition, I have this equation: $x-1=a(x^2+9)+b(x+1)$. I can easily set $x=-1$ and calculate $a=-\frac{1}{5}$. But how do I get $b$? I have tried putting the $a$ in and some random $x\neq -1$, but for each random $x$ I get a different value for $b$. Why is that so? And what is the proper method for calculating $b$?