What would the indefinite integral of 3xe^(x/3) + e^(4x)/sqrt(2) be?

Answer 1

You need to know 2 facts:

the integral of e^kx = e^kx/k

and you integrate xe^x by parts to get xe^x - e^x with u=x, du=1, dv=e^x and v=e^x

For this problem you have some nuisance coefficients to deal with ^{but that should now be no problem!}