What's the integral of e^(1+i)x dx? Please provide the full solution because I don't understand how to do this question at all.

I assume you mean the integral of e^[(1+i)x]

Since 1 + i is a constant, and the integral of e^ax = (1/a)e^ax for any constant a, the integral is

e^[(1+i)x]/(1+i)

= [(1-i)/2]*e^[(1+i)x]