Question

`\int\limits (8x)/(x^2+1) dx`

Answer 1

`\displaystyle \int~\cfrac{8x}{x^2+1}~dx~\hfill u=x^2+1\implies \cfrac{du}{dx}=2x\implies \cfrac{du}{2x}=dx \\\\\\ \displaystyle \int~\cfrac{8x}{u}\cdot \cfrac{du}{2x}\implies \int~\cfrac{4}{u}\cdot du\implies 4\int~\cfrac{1}{u}~du \\\\\\ 4\ln|u|+C\implies {\Large \begin{array}{llll} 4\ln|x^2+1|+C \end{array}}`