What is f(x) = int (x-2)/(x-1) dxf(x)=x2x1dx if f(2) = 0 f(2)=0?

1 Answer
Sep 30, 2017

f(x)=int(x-2)/(x-1)dxf(x)=x2x1dx
f(x)=int(x-1-1)/(x-1)dxf(x)=x11x1dx
f(x)=int(1+(-1)/(x-1))dxf(x)=(1+1x1)dx
f(x)=int1dx-int(1)/(x-1)dxf(x)=1dx1x1dx
f(x)=x-log(x-1)+cf(x)=xlog(x1)+c
c is constant of integration
to find the value of c we use f(2)=0f(2)=0
If f(2)=0f(2)=0
=>2-log(2-1)+c=02log(21)+c=0
=>2-log1+c=02log1+c=0
=>2-0+c=020+c=0
=>c=-2c=2

Hence
f(x)=x-log(x-1)-2f(x)=xlog(x1)2