If x+1 2 x-1 ~d x=f(x) 2 x-1 +C , where C is an arbitrary constant, then f(x) is equal to

Step-by-step solution

aligned & x+1 2 x-1 ~d x= t+1 2 +1 t ~d t[ Let 2 x-1=t] & = t+3 4+ t ~d t= 1 4 t ~d t+ 3 4 d t t & = 1 4 2 3 t^ 3 / 2 + 3 4 2 t^ 1 / 2 +C= 1 6 t t+9 +C & = 1 6 2 x-1 2 x-1+9 +C & = 1 3 (x+4) 2 x-1 +C & f(x)= 1 3 (x+4) aligned