Integrate ((x – frac{1}{x})^{2}) with respect to x.
-
A.
(frac{1}{3}(x – frac{1}{x})^{3} + c) -
B.
(frac{x^{3}}{3} – xsqrt{frac{1}{x^{3}}} + c) -
C.
(frac{x^{3}}{3} – 2x + frac{1}{x^{3}} + c) -
D.
(frac{x^3}{3} – 2x – frac{1}{x} + c)
Correct Answer: Option D
Explanation
((x – frac{1}{x})^{2} = x^2 – 2 + frac{1}{x^2})
(int (x^2 + frac{1}{x^2} – 2) mathrm {d} x)
= (int (x^2 + x^{-2} – 2) mathrm {d} x)
= (frac{x^3}{3} – 2x – frac{1}{x})