Question

$\int (\frac{1}{x}-x^2-\frac{1}{3})dx$ is equal to

• A. $\frac{x^2}{2}-\frac{x^3}{3}+c$
• B. $\ln |x|-\frac{x^3}{3}-\frac{1}{3}x+c$
• C. $x-\frac{x^2}{3}-\frac{x^2}{3}+c$
• D. $x-\frac{x^2}{2}-\frac{x^3}{3}+c$

Answer 1

The correct option is B $\ln |x|-\frac{x^3}{3}-\frac{1}{3}x+c$

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