Answer
$C(x)=5x+x^{2}+\ln x+994$
Work Step by Step
The marginal cost at production level of x is
$C'(x)=5+2x+\displaystyle \frac{1}{x}$
So, $C(x)$ is an antiderivative:
$C(x)=\displaystyle \int(5+2x+\frac{1}{x})dx$
$=5x+x^{2}+\ln|x|+D$
the production quantity x is a positive value, so we drop the absolute value brackets
$C(x)=5x+x^{2}+\ln x+D$
The indefinite integral gives us a collection of functions.
To find the exact function, we find $D.$
The text gives us:$\quad C(1)=1000$,
from which we find $D.$
$1000=5+1+\ln 1+D$
$994=D$
Thus,
$C(x)=5x+x^{2}+\ln x+994$
