If ∫x2-1x+12xx2+x+1dx=Atan-1x2+x+1x+c where c is real constant, then A=
12
3
2
1
Explanation for the correct option.
ddxtan-1x2+x+1x=11+x2+x+1x·12xx2+x+1x2x+1-x2+x+1x2=x2x+12xx2+x+1x2-1x2=x-12xx+1xx2+x+1=x2-12x+12xx2+x+1
Substituting this in the given equation, we get
x2-1x+12xx2+x+1=Ax2-12x+12xx2+x+1
Therefore, A=2
Hence, option C is correct.