Evaluate integral with quadratic expression without root in the denominator $$\int \frac{1}{x(x^2+1)}dx = ? $$ 
How to solve it? Expanding to $\frac {A}{x}+ \frac{Bx +C}{x^2+1}$ would be wearisome.

You can consider
$\displaystyle \frac{1}{x(x^2 + 1)} = \frac{1 + x^2 - x^2}{x(x^2 + 1)}$.
