Explanation

(c)
$\int_{}^{}{\frac{ax^{3} + bx^{2} + c}{x^{4}}\ dx}$
$= \int_{}^{}{\left\lbrack \frac{a}{x} + \frac{b}{x^{2}} + \frac{c}{x^{4}} \right\rbrack dx}$
$= a\int_{}^{}{\frac{1}{x}dx + b\int_{}^{}{x^{- 2}dx + c\int_{}^{}{x^{- 4}dx}}}$
$= a\log{x - bx^{- 1} - \frac{c}{3}x^{- 3} + k = a\log{x - \frac{b}{x} - \frac{c}{3x^{3}} + k}}$