\int\frac{x-2}{x^3}dx
źródło:
\int\frac{x-2}{x^3}dx=\int\frac{x}{x^3}dx-\int\frac{2}{x^3}dx=
=\int x^{-2}dx-\int2x^{-3}=\frac{x^{-1}}{-1}-\frac{2x^{-2}}{-2}+C=
=-x^{-1}+x^{-2}+C=-\frac{1}{x}+\frac{1}{x^2}+C=
=-\frac{x+1}{x^2}+C=\frac{1-x}{x^2}+C