∫(1+t^3)^1/2 dt

We can use the substitution u = t^3 to simplify the integral:

du/dt = 3t^2
dt = du/(3t^2)

Substituting these into the original integral, we get:

∫(1 t^3)^1/2 dt = ∫(1 u)^1/2 du/(3t^2)
= (1/3) ∫u^1/2 du
= (2/3) u^(3/2) + C
= (2/3) t^3/2 + C

Therefore, the solution to the integral is (2/3) t^3/2 + C.