If (x- 4 ) 2+ 2 x d x=- 1 2 ⁻¹(f(x))+C , then f(x)=

Step-by-step solution

aligned & I= (x- 4 ) 2+ 2 x d x=- 1 2 ⁻¹(f(x))+C & I= 1 2 x- x 1+( x+ x)^2 d x aligned On putting x+ x=t aligned & ( x- x) d x=d t & aligned I & =- 1 2 d t 1+t^2 =- 1 2 ⁻¹ t+C & =- 1 2 ⁻¹( x+ x)+C f(x) & = x+ x= 2 ( (x- 4 ) ) aligned aligned