Question

find the function f given that the slope of the tangent line to the graph of f at any point (x,f(x)) is f'(x) = (2/x) + 1, and the point (1,3) is on the graph of f

Answer 1

the "anti derivative" is
\[2\ln(x)+x+C\] and to find C replace x by 1, set the result = 3 and solve for C

Answer 2

\[2\ln(1)+1+C=3\]
\[1+C=3\]\[C=2\] and your function is
\[f(x)=2\ln(x)+x+2\]