Evaluate: ∫ (2x³ - 1)/(x⁴ + x) dx

$\int \frac{2x^3 - 1}{x^4 + x}\,dx$ Dividing both numerator and denominator by $x$ we get $= \int \frac{2x - \frac{1}{x^2}}{x^2 + \frac{1}{x}}\,dx$. Let $x^2 + \frac{1}{x} = t \Rightarrow \left(2x - \frac{1}{x^2}\right)dx = dt$ $= \int \frac{dt}{t}$ $= \log_e|t| + c$ $= \log_e\left|x^2 + \frac{1}{x}\right| + c$