let I=d

Open the brackets, we get

I={∫ e^x f(x) dx + ∫ e^x f^’(x) dx}

=U+∫ e^x f^’(x) dx

U=∫e^x f(x)dx

To solve U using integration by parts

U = f(x) ∫e^x dx - ∫[f^’(x) ∫e^x]

= f(x) e^x -∫ f^’(x) e^x

= U + ∫ e^x f^’(x) dx

I = e^x f(x) + ∫f^’(x) e^x dx - ∫ e^x f^’(x) dx

I=e^x f(x)+c