Take the integral:
integral(e^x x + e^x) dx
Integrate the sum term by term:
= integral e^x dx + integral e^x x dx
For the integrand e^x, integrate by parts, integral f dg = f g - integral g df, where
f = e^x, dg = dx, df = e^x dx, g = x:
= e^x x - integral e^x x dx + integral e^x x dx
Simplify:
Answer: |= e^x x + constant
