Answer
$F(x) = \frac{x}{5} - 2\ln|x| + C$, $x\ne0$
Work Step by Step
$f(x) = \frac{1}{5} - \frac{2}{x}$
Rewrite the second term as a product.
$f(x) = \frac{1}{5} - 2(\frac{1}{x})$
Rewriting the second term makes it easy to take the antiderivative (since we already know the antiderivative of $\frac{1}{x}$).
$F(x) = \frac{1}{5} - 2\ln|x|$
Now we take the antiderivative of the first term and add the constant.
$F(x) = \frac{x}{5} - 2\ln|x| + C$, $x\ne 0$
