Indefinite Integration

If $\int \frac{2 x+3}{(x-1)\left(x^2+1\right)} d x$

\(=\log _e\left\{(x-1)^{\frac{5}{2}}\left(x^2+1\right)^2\right\}-\frac{1}{2} \tan ^{-1} x+\mathrm{A}\)

where A is an arbitrary constant, then the value of $a$ is