Question

$\int 2x(x-x^{-3})dx$ is equal to

• A. $\frac{2x^3}{3}+\frac{2}{x}+c$
• B. $\frac{2x^3}{3}-\frac{2}{x}+c$
• C. $\frac{x^3}{3}-\frac{2}{x}+c$
• D. $\frac{x^3}{3}+\frac{2}{x}+c$

Answer 1

The correct option is A $\frac{2x^3}{3}+\frac{2}{x}+c$

$\int 2x(x-x^{-3})dx$
$=\int (2x^2-2x^{-2})dx$
$=\int 2x^{2}dx-\int 2x^{-2}dx$
$=\frac{2x^3}{3}-2\frac{x^{-2+1}}{-2+1}+c=$ $=\frac{2x^3}{3}+\frac{2}{x}+c$