I'm struggling to integrate $$\int{\frac{\sqrt{x+1}}{x^2}}$$ I already know the answer after i used by parts. But could this be found using substitution instead and not integration by parts?
I made $u=\sqrt{x+1}$ and got $$2\int{\frac{u^2}{(u^2-1)^2}}$$ and then used long division to integrate further. have i made a mistake?