Question

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

Answer 1

`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`