Question

$\int_{}^{}\frac{\mathbf{a}\mathbf{x}^{\mathbf{3}}\mathbf{+ b}\mathbf{x}^{\mathbf{2}}\mathbf{+ c}}{\mathbf{x}^{\mathbf{4}}}\mathbf{dx}$equals to

• A. $a\log x + \frac{b}{x^{2}} + \frac{c}{3x^{3}} + k$
• B. $a\log x + \frac{b}{x} - \frac{c}{3x^{3}} + k$
• C. $a\log x - \frac{b}{x} - \frac{c}{3x^{3}} + c$
• D. None of these

Answer 1

Answer: (C)

$a\log x - \frac{b}{x} - \frac{c}{3x^{3}} + c$

Answer 2

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