e^ x 2 e^ -x -e^x ~d x= ⁻¹(f(x))+C, (where C is constant of integration.) then f(2) has the value

Step-by-step solution

aligned & e^ x / 2 e^ -x -e^x ~d x= e^x ~d x 1- (e^x )^2 [ Multiplying N^r and D^r by e^ x 2 ] . & = d t 1-t^2 = ⁻¹ t+C= ⁻¹ (e^x )+C [ let e^x=t ] & f(x)=e^x & f(2)=e^2 aligned