What is f(x) = int (x-2)/(x-1) dx if f(2) = 0 ?

1 Answer
Sep 30, 2017

f(x)=int(x-2)/(x-1)dx
f(x)=int(x-1-1)/(x-1)dx
f(x)=int(1+(-1)/(x-1))dx
f(x)=int1dx-int(1)/(x-1)dx
f(x)=x-log(x-1)+c
c is constant of integration
to find the value of c we use f(2)=0
If f(2)=0
=>2-log(2-1)+c=0
=>2-log1+c=0
=>2-0+c=0
=>c=-2

Hence
f(x)=x-log(x-1)-2