What is ʃ e^(1/2)x (dx)?

Answer 1

∫e^udu = e^u + C

Let u = (1/2)x. Then du = (1/2)dx. So, dx = 2du.

∫e^(1/2)xdx = ∫e^u(2du) = 2∫e^udu = 2e^u + C = 2e^(1/2)x + C

In general, for any constant k≠0, ∫e^kxdx = (1/k)e^kx + C.