The marginal profit of a certain company is given by $$y ' (x) = \frac{100}{32-4x}$$ where $x$ represents the amount of money (in thousands of dollars) that the company spends in advertising. Find the profit for an advertising expenditure of $3000$ if the profit is $\$1000$ when nothing is spent on advertising.
Says the answer for $\$3,000$ is $1011.75$ But I don't know how to get to that answer. Thank you.
Writing $$dy=\frac{25}{8-x}dx$$ and integrating we obtain $$y(x)=C-25\log|8-x|$$