Question

Khẳng định nào sau đây đúng?

A. \(\int\left(x-\dfrac{1}{x}\right)^2dx=\dfrac{x^3}{3}-2x-\dfrac{1}{x}+C.\)

B. \(\int\left(x-\dfrac{1}{x}\right)^2dx=\dfrac{x^3}{3}-2x+\dfrac{1}{x}+C.\)

C. \(\int\left(x-\dfrac{1}{x}\right)^2dx=\dfrac{1}{3}\left(x-\dfrac{1}{x}\right)^3+C.\)

D. \(\int\left(x-\dfrac{1}{x}\right)^2dx=\dfrac{1}{3}\left(x-\dfrac{1}{x}\right)^3\left(1+\dfrac{1}{x^2}\right)+C.\)

Answer 1

Ta có

\(\int {{{\left( {x - \frac{1}{x}} \right)}^2}dx}  = \int {\left( {{x^2} - 2 + \frac{1}{{{x^2}}}} \right)dx}  = \int {{x^2}dx}  - 2\int {dx}  + \int {\frac{1}{{{x^2}}}dx}  = \frac{{{x^3}}}{3} - 2x - \frac{1}{x} + C\)

Vậy đáp án đúng là A.