x^2-4 x^4+9 x^2+16 ~d x= ⁻¹( f (x))+ c ( where c is a constant of integration), then value of f(2) is

Step-by-step solution

Let I= x^2-4 x^4+9 x^2+16 ~d x aligned & = 1- 4 x^2 x^2+ 16 x^2 +9 d x & = 1- 4 x^2 (x+ 4 x )^2+1 d x aligned Put x+ 4 x = t (1- 4 x^2 ) d x= dt aligned I & = dt t ^2+1 & = ⁻¹ t + c & = ⁻¹ (x+ 4 x )+ c aligned array ll & f (x)=x+ 4 x & f (2)=2+2=4 array