答：
设t=√(x-1),x=t^2+1,dx=2tdt
∫ e^[√(x-1)] dx
=∫ e^t *2t dt
=2te^t-2∫e^t dt
=2te^t-2e^t+C
=2√(x-1)*e^[√(x-1)-2e^[√(x-1)]+C