If f'(x) = ( x +1)e^ x x and f(0) = e then f(1) =

Step-by-step solution

f(x) = ( x +1)e^ x x dx Let x = t 1 2 x dx = dt dx x = 2 dt f(x) = (t+1)e^t (2 dt) = 2 (t+1)e^t dt f(x) = 2 t e^t + C Substituting t = x : f(x) = 2 x e^ x + C Given f(0) = e : 2(0)e^0 + C = e C = e Thus, f(x) = 2 x e^ x + e For x = 1 : f(1) = 2(1)e^1 + e = 3e Answer: 3e