Evaluate the definite integral $\begin{align*}\int\limits_0^1\frac{2x+3}{5x^2+1}dx \end{align*}$

Question

$\begin{array}{1 1}\large \frac{1}{5} \log 6+\large \frac{3}{\sqrt 5}\tan^{-1}(\sqrt 5) \\ \large \frac{1}{5} \log 3-\large \frac{5}{\sqrt 3}\tan^{-1}(\sqrt 5) \\ \large \frac{1}{3} \log 3+\large \frac{5}{\sqrt 3}\tan^{-1}(\sqrt 3) \\ \large \frac{1}{3} \log 3-\large \frac{5}{\sqrt 3}\tan^{-1}(\sqrt 3)\end{array}$