Question

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

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

Answer 1

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

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