Find f by solving the initial-value problem. (Remember to use absolute values where appropriate.)

Question

f '(x) = (x + 1)/x ; f(1) = 5
f(x)=

Answer 1

f '(x) = (x + 1)/x
= x/x + 1/x
= 1 + 1/x
f(x) = x + ln|x| + c
f(1) = 1 + 0 + c = 5

c = 4

f(x) = x + ln|x| + 4