x3+5x+1x3≡1+5x2+1x3\frac{x^{3}+5x+1}{x^{3}} \equiv 1 + \frac{5}{x^{2}} + \frac{1}{x^{3}}x3x3+5x+1≡1+x25+x31
≡∫(1+5x2+1x3)dx=∫(1+5x−2+x−3)dx\equiv \int \left(1 + \frac{5}{x^{2}} + \frac{1}{x^{3}}\right) dx = \int (1 + 5x^{-2} + x^{-3}) dx≡∫(1+x25+x31)dx=∫(1+5x−2+x−3)dx
= (x−5x−1−12x−2+c)\left(x - 5x^{-1} - \frac{1}{2} x^{-2} + c\right)(x−5x−1−21x−2+c)
= x−5x−12x2+cx - \frac{5}{x} - \frac{1}{2x^{2}} + cx−x5−2x21+c.
