I was helping my friend with her integration problems, and both she and I got stuck on this problem. Anyone can gives me a hand. I'd really appreciate it. We were trying to integrate $\displaystyle \frac{\sqrt(x^2+1)}{x^2}$. We tried to do the following substitution. Let $\displaystyle x=tan\theta$ then, $\displaystyle dx=sec^2\theta$. So we have $\displaystyle \int \frac{(tan^2\theta +1)sec^2\theta}{tan^2\theta}=\int \frac{sec^3\theta}{tan^2\theta} $. Then since $\displaystyle tan^2\theta=sec^2\theta-1$, we substitute this into the expression, but got nowhere.