₁^ e e ^x x (1+x x) d x=

Step-by-step solution

To evaluate the integral ₁^ e e ^x x (1+x x) d x , observe that the integrand simplifies to e ^x ( x + 1 x ) . This matches the standard form e ^x (f(x) + f'(x)) with f(x) = x , whose derivative is f'(x) = 1 x . The antiderivative is e ^x x , so evaluating from 1 to e yields e ^ e e - e ^1 1 = e ^ e - 0 = e ^ e . The result corresponds to option A .