Source TeX:

\displaystyle\left. \begin{aligned}\begin{split}\int \dfrac{ax+b}{x^{2}+px+q} dx&=\int \dfrac{ax+b}{\left( x-\alpha\right) ^{2}+\beta^{2}} dx\\&=\int \dfrac{Mt+N}{t^{2}+1}dt\\&= \int \dfrac{Mt}{t^{2}+1}dt+\int \dfrac{N}{t^{2}+1}dt\\&= \dfrac{M}{2} \ln \left( t^{2}+1\right) +N\, \arctan(t) +c, \; c\in \mathbb{R}.\end{split}\end{aligned}\right.