I am trying to get the first four terms of the Maclaurin Series for the following functiong:

integral from 0 to x of sqrt(1+t^3) dt

Sadly, I'm stuck trying to find the integral so that I can get the first f(0) term. Using u-substitution I get:

u = 1 + t^3

du = 3t^2 dt

dt= du / 3t^2

I think that I need to put 3t^2 in terms of u to be able to continue with the integration, but I cannot see a connection. If I make u = t^3 then would 3t^2 = 3u^2/3 ??

thanks!