Question

$\int \frac{x^5+x^{-2}+2}{x^2}dx$

Answer 1

$$\begin{gathered} \int \left(\frac{x^5+x^{-2}+2}{x^2}\right)dx \\ =\int \left(\frac{x^5}{x^2}+\frac{x^{-2}}{x^2}+\frac{2}{x^2}\right)dx \\ =\int \left(x^3+x^{-4}+2x^{-2}\right)dx \\ =\frac{x^{3+1}}{3+1}+\frac{x^{-4+1}}{-4+1}+2\frac{x^{-2+1}}{-2+1}+\mathrm{C} \\ =\frac{x^4}{4}-\frac{1}{3x^3}-\frac{2}{x}+\mathrm{C} \end{gathered}$$